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In mathematics, and especially in homotopy theory, a crossed module consists of groups G {\displaystyle G} and H {\displaystyle H} , where G {\displaystyle
Crossed_module
In mathematics, a module that has a basis
mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the
Free_module
British mathematician (1904–1960)
conjecture led to the creation of the Whitehead manifold. The definition of crossed modules is due to him. He also made important contributions in differential
J._H._C._Whitehead
\mathbb {Z} _{4})\cong \mathbb {Z} /2} . Because this is not a trivial crossed-module, it's postnikov invariant is 1 {\displaystyle 1} , giving a homotopy
Double_groupoid
Mathematical theorem
the category of groupoids turns out to be equivalent to the notion of crossed module. This leads to the idea of using multiple groupoid objects in homotopy
Eckmann–Hilton_argument
Modular space station in low Earth orbit
plans for the ISS include the addition of at least one module, the Payload Power Thermal Module by Axiom Space, forming the commercial segment of the station
International_Space_Station
properties of 2-groups are already known. 2-groups can be described using crossed modules and their classifying spaces. Essentially, these are given by a quadruple
N-group_(category_theory)
Enterprise resource planning by SAP SE
management, and simplified landscape deployment. The update also improved cross-module traceability, allowing audit and change tracking across distributed systems
SAP_S/4HANA
Study of categorified structures
theory Grothendieck topology Topological dynamics Categorical dynamics Crossed module Pseudoalgebra 2-ring Lie n-algebra "Double Categories and Pseudo Algebras"
Higher-dimensional_algebra
Algebraic construct classifying topological spaces
n\geq 3} but for n = 2 {\displaystyle n=2} form the top group of a crossed module with bottom group π 1 ( A ) . {\displaystyle \pi _{1}(A).} There is
Homotopy_group
Electronics module
A power module or power electronic module provides the physical containment for several power components, usually power semiconductor devices. These power
Power_module
Organizing code into modules
into independent modules, each providing an aspect of a computer program in its entirety without providing other aspects. A module interface expresses
Modular_programming
Scheme-based programming language implementation
scrutinizer does not allow cross-module flow analysis, so it can only be used to optimize code that's part of one compiling unit (or module). CHICKEN Scheme was
Chicken (Scheme implementation)
Chicken_(Scheme_implementation)
Motor vehicle platform
The Common Module Family (CMF) is a modular architecture concept jointly developed by car manufacturers Nissan and Renault through their Renault–Nissan–Mitsubishi
Renault–Nissan Common Module Family
Renault–Nissan_Common_Module_Family
Branch of mathematics
theory Pursuing Stacks Shape theory Moduli stack of formal group laws Crossed module Milnor's theorem on Kan complexes Fibration of simplicial sets Shape
Homotopy_theory
Vacuum tube used in transmitters
A crossed-field amplifier (CFA) is a specialized vacuum tube, first introduced in the mid-1950s and frequently used as a microwave amplifier in very-high-power
Crossed-field_amplifier
Bialgebra Bicategory Convolution product Crossed module Double groupoid Higher-dimensional algebra Hopf algebra Module (mathematics) Ring (mathematics) Mosa
R-algebroid
Python module for writing video games
Pygame is a cross-platform set of Python modules designed for writing video games. It includes computer graphics and sound libraries designed to be used
Pygame
addresses of externally referenced objects and functions, various kinds of cross module checks (e.g. type checks on externally visible identifiers and in some
Link_time
Branch of mathematics
method of simplicial approximation. It contains a lot of material on crossed modules. Fraleigh, John B. (1976), A First Course In Abstract Algebra (2nd ed
Algebraic_topology
Gives a homomorphism from homotopy groups to homology groups
homotopical excision theorem, involving induced modules for n > 2 {\displaystyle n>2} (crossed modules if n = 2 {\displaystyle n=2} ), which itself is
Hurewicz_theorem
German 155 mm self-propelled howitzer
developed by Krauss-Maffei Wegmann (now KNDS Deutschland). The RCH 155 Module takes the firepower and the range of the PzH 2000 by using its gun (155
RCH_155
Multinational wheeled armoured fighting vehicle
drive module and interchangeable mission modules which allow several configurations to meet different operational requirements. The drive module has been
Boxer (armoured fighting vehicle)
Boxer_(armoured_fighting_vehicle)
identified with crossed modules, and are most often studied in that form. Thus, 2-groups in general can be seen as a weakening of crossed modules. Every 2-group
2-group
Tools for studying groups based on techniques from algebraic topology
actions of a group G in an associated G-module M to elucidate the properties of the group. By treating the G-module as a kind of topological space with elements
Group_cohomology
System-on-a-chip microcontroller model with Wi-Fi
community in August 2014 via the ESP-01 module, made by a third-party manufacturer Ai-Thinker. This small module allows microcontrollers to connect to a
ESP8266
Hypothesis in mathematical category theory
is still open.[citation needed] See also: Eilenberg–MacLane space, crossed module. Algebraic homotopy N-group (category theory) Pursuing Stacks Quasi-category
Homotopy_hypothesis
to optimize across functions and modules. Target-independent optimizations supported by vbcc include: cross-module function inlining partial inlining
Vbcc
of crossed groups over a site". arXiv:1702.02128 [math.AG]. - gives techniques for defining sheaf cohomology with coefficients in a crossed module, or
Abelian_2-group
Family of file formats
Module file (MOD music, tracker music) is a family of music file formats originating from the MOD file format on Amiga systems used in the late 1980s.
Module_file
Rotating circular machine part with teeth that mesh with another toothed part
described in the equations above) is not zero, the shafts are crossed. For shafts crossed at right angles, the helix angles are of the same hand because
Gear
American astronaut and lunar explorer (1930–2018)
then commanded the 1966 Gemini 10 mission. In 1969, he flew as command module pilot on Apollo 10, and became the first person to orbit the Moon alone
John_Young_(astronaut)
Polyhedron whose vertices represent permutations
Graduate Texts in Mathematics 152. Huebschmann, J. (2012), "Braids and crossed modules", Journal of Group Theory, 15: 57–83, arXiv:0904.3895, doi:10.1515/JGT
Permutohedron
Programming language
In computing, ATS (Applied Type System) is a multi-paradigm, general-purpose, high-level, functional programming language. It is a dialect of the programming
ATS_(programming_language)
Switch between light-conducting fiber circuits
demultiplexers. The electronic signals are then switched by an electronic switch module. Finally, the switched electronic signals are converted back into optical
Optical_cross-connect
Vector space equipped with a bilinear product
with "commutative ring" and "module". Unital zero algebras allow the unification of the theory of submodules of a given module and the theory of ideals of
Algebra_over_a_field
Primary US ISS module
The Destiny module, also known as the U.S. Lab, is the primary operating facility for U.S. research payloads aboard the International Space Station (ISS)
Destiny_(ISS_module)
methods". Cubical omega-groupoids, higher homotopy groupoids, crossed modules, crossed complexes and Galois groupoids are key concepts in developing applications
Nonabelian_algebraic_topology
Web browser developed by Cliqz GmbH
Cliqz was a privacy-oriented web browser and search engine developed by Cliqz GmbH and majority-owned by Hubert Burda Media. It was available as a desktop
Cliqz
Computer memory module
A SIMM (single in-line memory module) is a type of memory module used in computers from the early 1980s to the early 2000s. It is a printed circuit board
SIMM
a module (0.33 m) tall. The width of these letters is three-tenths of a module (0.30 m). The conjunction E has a height of three-tenths of a module (0
Flag_of_Brazil
Brown, Ronald; Spencer, Christopher B. (1976). "Double groupoids and crossed modules" (PDF). Cahiers de Topologie et Géométrie Différentielle Catégoriques
Elementary theory of abstract categories
Elementary_theory_of_abstract_categories
Infinite-dimensional group in topology
Elliptic cohomology String bordism Jurco, Branislav (August 2011). "Crossed Module Bundle Gerbes; Classification, String Group and Differential Geometry"
String_group
American astronaut (1930–2012)
Module (LM) pilot Buzz Aldrin became the first people to land on the Moon, and the next day they spent two and a half hours outside the Lunar Module Eagle
Neil_Armstrong
shooting occurred at Robb Elementary School when an 18 year old gunman crossed the grounds of the school in Uvalde, Texas, without being confronted and
List of The Weekly with Charlie Pickering episodes
List_of_The_Weekly_with_Charlie_Pickering_episodes
Free software music tracker
for composing music in the MOD and XM module file formats. It is a clone that attempts to recreate the module replay and user experience of the popular
MilkyTracker
In-development multiplayer space game
known as "modules", to provide players with the opportunity to experience gameplay features prior to release. The "Persistent Universe" module was made
Star_Citizen
Microwave network module
A phase shift module is a microwave network module which provides a controllable phase shift of the RF signal. Phase shifters are used in phased arrays
Phase_shift_module
History of maths
properties such as a monoidal structure. 1949 John Henry Whitehead Crossed modules. 1949 André Weil Formulates the Weil conjectures on remarkable relations
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Army training program
the basic fundamentals of advanced special operations. Module J – MOS Cross Training: This module provides officers with knowledge and education of the
United States Army Special Forces selection and training
United_States_Army_Special_Forces_selection_and_training
Open source web server and a reverse proxy server
the addition of dynamic module loading. However, the modules still must be compiled at the same time as Nginx, and not all modules are compatible with this
Nginx
on standard practice. A crossed helical gear is a gear that operate on non-intersecting, non-parallel axes. The term crossed helical gears has superseded
List_of_gear_nomenclature
Computer screensaver software
slider in the Flying Toasters module enabled users to adjust the toast's darkness, and an updated Flying Toasters Pro module added a choice of music—Richard
After_Dark_(software)
Baked item for Easter season
arms crossed and hands placed on opposite shoulders. Hot cross buns are popular during Lent. The cross of course reminds the eater of Christ's cross. The
Hot_cross_bun
Internal code for computer graphics
support that module's features, which are classified through capabilities, and declared early in the module. A validator can confirm that the module uses only
Standard Portable Intermediate Representation
Standard_Portable_Intermediate_Representation
US Navy fast attack submarine class
section form a module which, when joined with other modules, forms a Virginia-class submarine. Block I boats were built in 10 modules with each submarine
Virginia-class_submarine
Microwave Power Module Panel, supported by the US Naval Research Laboratory. While the eventual goal was to design a power module with a cross section as small
Microwave_power_module
Proposed Russian space station
Soviet space station project which began in February 1976. Some of the modules built for Mir-2 have been incorporated into the International Space Station
Mir-2
Filtration by force through a semipermeable membrane
design is conceptually similar to the tubular module with a shell and tube arrangement. A single module can consist of 50 to thousands of hollow fibres
Ultrafiltration
Industrial Automation Software
and FactoryPMI became the SQL Bridge Module and Vision Module, respectively. The Reporting Module and OPC-UA Module were included in the initial release
Inductive_Automation
German football player and manager (1897–1977)
Josef "Sepp" Herberger (28 March 1897 – 28 April 1977) was a German football player and manager. He is most famous for being the manager of the West Germany
Sepp_Herberger
EDA/CAD software for creating schematic diagrams and printed circuit boards
delivers a number of features for visual and logical pin connections. Cross-module management ensures that principal circuits can be easily converted into
DipTrace
American dark electronic band
Module is an American dark electronic band founded in 1999 from Orlando, Florida. Since 2006 they have been based out of Washington state. God Module
God_Module
Lightweight programming language
values at run time), coroutines (cooperative multitasking) and dynamic module loading. The classic "Hello, World!" program can be written as follows,
Lua
American multinational technology company
Linux <open-source GPU kernel modules> under dual GPL/MIT licensing, allowing developers to inspect the driver module code and contribute improvements
Nvidia
Building construction standard for positioning
surfaces, widths of shelves and kitchen components are multiples of the basic module. ISO 2848 is based on multiples of 300 mm and 600 mm. As dimensions increase
ISO_2848
Importation without permission from intellectual property owner
A parallel import is a non-counterfeit product imported from another country without the permission of the intellectual property owner. Parallel imports
Parallel_import
Malicious website exploit where unauthorized commands are transmitted from a trusted user
sent by untrusted sites to trusted ones. The Application Boundary Enforcer module in NoScript also blocks requests sent from internet pages to local sites
Cross-site_request_forgery
American astronaut and lunar explorer (1934–2017)
times and to the Moon twice: as pilot of Gemini 9A in June 1966, as Lunar Module pilot of Apollo 10 in May 1969, and as commander of Apollo 17 in December
Gene_Cernan
Applies an electric current to heat or cool materials
effect). A thermoelectric module is made from three components: the conductors, the legs, and the substrate. Many of these modules are connected electrically
Thermoelectric_heat_pump
Open source web server
provided by modules, which are plugins that extend Caddy's configuration structure; for example, the HTTP server is a module. Caddy modules implement various
Caddy_(web_server)
Role-playing game published using the Open Game License
Dungeons & Dragons modules in content and style. The design ethos is summed up by the following statement included in every DCC module, regardless of which
Dungeon_Crawl_Classics
Type of nuclear fission reactor
deliver an electrical power output as low as 10 MWe and up to 300 MWe per module. Reactors below 10 MWe in capacity are considered nuclear microreactors
Small_modular_reactor
American reality television series episodes
2020 (2020-12-21) Items appraised include a set of diagrams for the Apollo 11 Lunar Module Eagle; a 1950s Martin tiple; a collection of 19th-century pistols that belonged
List_of_Pawn_Stars_episodes
British mathematician
Her first paper in homological algebra (Some algebraic properties of crossed modules) was published in 1951 and she earned her DPhil for her thesis Modern
Anne_Cobbe
Argentine footballer (born 1987)
pitch and curl shots on goal with his left foot, rather than predominantly cross balls for teammates. Under Guardiola and subsequent managers, he most often
Lionel_Messi
Compiler that optimizes generated code
units which allows it to perform more aggressive optimizations like cross-module inlining and devirtualization. Machine code optimization involves using
Optimizing_compiler
Spanish footballer (born 2007)
he also has the ability to play outswinging crosses to the far post. His ability to produce accurate crosses with the outside of his foot (known as a trivela)
Lamine_Yamal
Originally applied specifically to undocumented Mexican migrant workers who had crossed the United States border via the Rio Grande river to find work in the United
List_of_ethnic_slurs
Statistical Survey
http://www.gesis.org/issp/modules/ GESIS ISSP Modules by Year http://www.gesis.org/issp/modules/issp-modules-by-year/ GESIS ISSP Modules By Topic http://www
International Social Survey Programme
International_Social_Survey_Programme
International standard for mounting equipment
generally use "modules" as a width unit, one module being 18 mm wide. For example, a small device (e.g. a circuit breaker) may have a width of 1 module (18 mm
DIN_rail
Concept in aspect-oriented software development
aspect-oriented software development, cross-cutting concerns are aspects of a program that affect several modules, without the possibility of being encapsulated
Cross-cutting_concern
lying down… especially when he discovers a pair of robotic arms hidden in a module that fell out of the robot! 56c 4c "Tai Chi Lemmings" Idriss Benseghir Idriss
List of Grizzy & the Lemmings episodes
List_of_Grizzy_&_the_Lemmings_episodes
American astronaut (1930–2021)
April 28, 2021) was an American astronaut who flew the Apollo 11 command module Columbia around the Moon in 1969 while his crewmates, Neil Armstrong and
Michael_Collins_(astronaut)
JavaScript runtime environment
using JavaScript and a collection of "modules" that handle various core functionalities.[excessive citations] Modules are provided for file system I/O, networking
Node.js
or “make an earnest attempt to achieve.” Both the US Apollo 15's Lunar Module and a Space Shuttle were named Endeavour and accomplished bold discoveries
List of minor planets: 470001–471000
List_of_minor_planets:_470001–471000
Free and open-source software and server
easier to include modules/plugins for new file formats, codecs, interfaces, or streaming methods. VLC 1.0.0 has more than 380 modules. The VLC core creates
VLC_media_player
Modules used in early PDP computers
A DEC System Modules (originally known as System Building Blocks; the name was changed around 1961) are a DEC modular digital logic family which preceded
DEC_System_Module
Lack of confidence about one's way of speaking
Linguistic insecurity comprises feelings of anxiety, self-consciousness, or lack of confidence in the mind of speakers surrounding their use of language
Linguistic_insecurity
Borehole in Russia, deepest on Earth
international geophysical experiment obtained a reflection seismic crustal cross-section through the well. The Kola-92 working group consisted of researchers
Kola_Superdeep_Borehole
American multinational technology company
employees. In September 2025 Google opened their £735m AI Centre in Waltham Cross, Hertfordshire and announced their plans for £5 bn investment in AI research
Object-oriented framework for software development
into individual modules. With Qt 5.0 the architecture was modularized even further. Qt is now split into essential and add-on modules. Qt classes by default
Qt_(software)
Financial products and services that conform to Sharia (Islamic law)
15 January 2018. Retrieved 28 September 2017. Honohon, Patrick. 2007. "Cross-Country Variations in Household Access to Financial Services." Presented
Islamic finance products, services and contracts
Islamic_finance_products,_services_and_contracts
Indian lunar mission (2023–Present)
over the landing site, twelve days after landing. The orbiting propulsion module remained operational and was repurposed for scientific observations of Earth;
Chandrayaan-3
1948 child murder in Blackburn, England
murderer had evidently entered the hospital. None of these experts were cross-examined by Griffiths' defence counsel. During the trial, Griffiths' defence
Murder_of_June_Anne_Devaney
Data interface description language
especially in cryptography. Protocol developers define data structures in ASN.1 modules, which are generally a section of a broader standards document written
ASN.1
2019 American science fiction drama
season 5), an astronaut and Ed's best friend, based on Apollo 10's Lunar Module pilot Gene Cernan Sarah Jones as Tracy Stevens (seasons 1–2), Gordo's wife
For_All_Mankind_(TV_series)
Graphical user interface library
resource provider is cross-platform and provides standard file-access mechanics for loading resources. An optional minizip module enables resource-loading
CEGUI
Concept in cognitive psychology
A cognitive module in cognitive psychology is a specialized tool or sub-unit that can be used by other parts to resolve cognitive tasks. It is used in
Cognitive_module
Country in Eurasia from 1922 to 1991
in operation from 1986 to 1998. Gradually, other modules were added to it, including American modules. However, the station deteriorated rapidly after
Soviet_Union
CROSSED MODULE
CROSSED MODULE
Girl/Female
Spanish
Crowned.
Surname or Lastname
English
English : variant of Cruse.Americanized spelling of German and Jewish Kraus.
Surname or Lastname
English and French
English and French : variant spelling of Crozier.
Surname or Lastname
English
English : variant of Crossley, also established as a surname in Ireland.
Male
Italian
Short form of Italian Crocifisso, or Croccifixio, CROSS means "cross; crucifix" or "way of the cross."
Surname or Lastname
English
English : unexplained. Perhaps a variant of Cripsey, habitational name from a place of this name in Lincolnshire.
Boy/Male
Australian, Gaelic, Scottish
Headland
Surname or Lastname
English
English : variant spelling of Cressy or possibly of Creasy.Probably also an altered spelling of German Kresse or Kresser.
Boy/Male
Australian, French, Greek
Victorious; Crowned; Crucifixion; Cross
Boy/Male
English
Meadow with a cross.
Surname or Lastname
English
English : habitational name from either of two places in West Yorkshire named Crossley, from Old English cros ‘cross’ + lēah ‘woodland clearing’.
Boy/Male
English
Meadow with a Cross
Surname or Lastname
English
English : topographic name for someone who lived near a stone cross set up by the roadside or in a marketplace, from Old Norse kross (via Gaelic from Latin crux, genitive crucis), which in Middle English quickly and comprehensively displaced the Old English form crūc (see Crouch). In a few cases the surname may have been given originally to someone who lived by a crossroads, but this sense of the word seems to have been a comparatively late development. In other cases, the surname (and its European cognates) may have denoted someone who carried the cross in processions of the Christian Church, but in English at least the usual word for this sense was Crozier.Irish : reduced form of McCrossen.In North America this name has absorbed examples of cognate names from other languages, such as French Lacroix.
Boy/Male
American, British, English
From the Cross Meadow
Boy/Male
British, English, Scandinavian
At the Cross
Surname or Lastname
German
German : habitational name from a place so named in East Prussia.English : possibly a variant spelling of Rosson.
Surname or Lastname
English
English : unexplained.Possibly an Americanized spelling of Swiss German Krüsi, a variant of Kruse, or Kriesi, a variant of Kries.
Surname or Lastname
English
English : perhaps a habitational name (reduced form) from Costessey in Norfolk, named with an Old English or Old Norse personal name Cost + Old English ēg ‘island’, ‘dry ground in a marsh’.Americanized spelling of French Cossé (see Cosse).
Boy/Male
English
By the cross.
Surname or Lastname
English and Irish
English and Irish : variant spelling of Cross.
CROSSED MODULE
CROSSED MODULE
Boy/Male
Hindu
Ocean
Boy/Male
Tamil
Khemprakash | கேமபà¯à®°à®•à®¾à®·
Welfare
Boy/Male
Indian, Punjabi, Sikh
Cherishing Peace and Tranquillity
Female
Hindi/Indian
(विजया) Hindi unisex name VIJAYA means "victory." In mythology, this is the name of a son of Krishna, and another name for the goddess Durga.
Boy/Male
Hindu
Without a superior
Girl/Female
Hindu, Indian, Sindhi
Guide to Righteousness
Boy/Male
Muslim
Lord and master
Boy/Male
Hindu, Indian
Courageous; Charioteer of Krishna; Arjuna
Boy/Male
Muslim
Gift. Favor.
Boy/Male
Tamil
Lohendra | லோஹேஂதà¯à®°
Lord of three worlds
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
CROSSED MODULE
n.
See Crosslet.
n.
A beam or bar across the head or end of a rod, etc., or a block attached to it and carrying a knuckle pin; as the solid crosspiece running between parallel slides, which receives motion from the piston of a steam engine and imparts it to the connecting rod, which is hinged to the crosshead.
a.
With arms crossed.
n.
A pilgrim bearing or wearing a cross.
v. t.
To make the sign of the cross upon; -- followed by the reflexive pronoun; as, he crossed himself.
a.
Crossed; intersected.
a.
Crowded; compact; dense; pressed together.
a.
Covered with hoarfrost or anything resembling hoarfrost; ornamented with frosting; also, frost-bitten; as, a frosted cake; frosted glass.
a.
False; dishonest; fraudulent; as, crooked dealings.
a.
Having a crown shaped like a steeple; as, a steeple-crowned hat; also, wearing a hat with such a crown.
n.
A small cross.
a.
Bearing a steeple; as, a steeple-crowned building.
n.
One who cross-examines or conducts a crosse-examination.
imp. & p. p.
of Cross
a.
Having the legs crossed.
a.
Incrusted; covered with, or containing, crust; as, old, crusted port wine.
a.
Crossed again; -- said of a cross the arms of which are crossed. SeeCross-crosslet.
n.
A cross having the three upper ends crossed, so as to from three small crosses.
a.
Clad or crowned with pine trees; as, pine-clad hills.
n.
The state of being closely surrounded, crowded, or pressed, as by ice.