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Category whose only morphisms are the identity morphisms
In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: homC(X, X) = {idX}
Discrete_category
Topics referred to by the same term
integrated circuit Discrete group, a group with the discrete topology Discrete category, category whose only arrows are identity arrows Discrete mathematics
Discrete
Conversion of continuous functions into discrete counterparts
modification of variable or category granularity, as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous
Discretization
Collection of objects and morphisms
class of categories. Any class can be viewed as a category whose only morphisms are the identity morphisms. Such categories are called discrete. For any
Category_(mathematics)
Mathematical concept
colimits of diagrams indexed by discrete categories. Copowers are colimits of constant diagrams from discrete categories. Coequalizers are colimits of a
Limit_(category_theory)
Type of topological space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous
Discrete_space
Indexed collection of objects and morphisms in a category
diagram A _ {\displaystyle {\underline {A}}} . If J is a (small) discrete category, then a diagram of type J is essentially just an indexed family of
Diagram_(category_theory)
Type of topological group
is an isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying
Discrete_group
Contrast of one emotion from another
to varying degrees in a non-verbal manner. Each emotion acts as a discrete category rather than an individual emotional state. Humans' subjective experience
Emotion_classification
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
Generalized object in category theory
{J} } as the discrete category with two objects, so that C J {\displaystyle \mathbf {C} ^{\mathbf {J} }} is simply the product category C × C . {\displaystyle
Product_(category_theory)
category J is connected if each functor from J to a discrete category is constant. In some cases it is convenient to not consider the empty category to
Connected_category
Types of numerical variables in mathematics
mathematics and statistics, a quantitative variable may be continuous or discrete. If it can take on two real values and all the values between them, the
Continuous or discrete variable
Continuous_or_discrete_variable
Category equipped with involution
a monoid with involution, because of the dagger. A discrete category is trivially a dagger category. A groupoid (and as trivial corollary, a group) also
Dagger_category
discrete A category is discrete if each morphism is an identity morphism (of some object). For example, a set can be viewed as a discrete category. distributor
Glossary_of_category_theory
Special objects used in (mathematical) category theory
objects in a category C may also be defined as limits of the unique empty diagram 0 → C. Since the empty category is vacuously a discrete category, a terminal
Initial_and_terminal_objects
Table that summarizes data from another table
spreadsheet, or business intelligence program) within one or more discrete categories. The aggregations or summaries of the groups of the individual terms
Pivot_table
Construction in category theory
that here we have morphisms as well. Thus, for example, when J is a discrete category, it corresponds most closely to the idea of an indexed family in set
Cone_(category_theory)
Discrete categories of objects such as faces, body parts, tools, animals and buildings have been associated with preferential activation in specialised
Neural processing for individual categories of objects
Neural_processing_for_individual_categories_of_objects
Type of topology in mathematics
denote its full subcategory consisting of Alexandrov-discrete spaces. Let Preord denote the category of preordered sets consisting of preordered sets with
Alexandrov_topology
Most general completion of a commutative square given two morphisms with same codomain
containing only the two objects X and Y, and no arrows between them (a discrete category), thus "forgetting" the morphisms f and g and the object Z from the
Pullback_(category_theory)
Type of chart
charts. A bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents
Bar_chart
Discrete-variable probability distribution
gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function
Probability_mass_function
Mathematical structures in category theory
{\displaystyle C} , D {\displaystyle D} ). If I {\displaystyle I} is a small discrete category (i.e. its only morphisms are the identity morphisms), then a functor
Functor_category
Social group defined by shared traits
do entail social processes of exclusion and incorporation whereby discrete categories are maintained despite changing participation and membership in the
Ethnicity
Type of monoidal category in category theory
appropriate symmetric monoidal categories of vector spaces under tensor product. Further examples of PROPs: the discrete category N {\displaystyle \mathbb {N}
PROP_(category_theory)
Theory that seeks to organize subjective feelings into discrete categories
interchangeably with emotions or subjectively experienced feelings, into discrete categories and to typify their physiological, social, interpersonal, and internalized
Affect_theory
Scale for measuring sexual orientation
goats. It is a fundamental of taxonomy that nature rarely deals with discrete categories... The living world is a continuum in each and every one of its aspects
Kinsey_scale
the matrix ring R n × n {\displaystyle R^{n\times n}} . If C is a discrete category, then RC may be seen as the ring of functions C → R {\displaystyle
Category_algebra
Set of features that characterize human language
quantities by varying how loudly one pronounces the /s/. Loudness can be a discrete category, as a form of stress, while the more continuous and impressionistic
Hockett's_design_features
Discrete device in an electronic system
An electronic component is any basic discrete electronic device or physical entity part of an electronic system used to affect electrons or their associated
Electronic_component
Japanese comics genre
released as early as the 1920s, sports manga did not emerge as a discrete category until the early 1950s. The genre achieved prominence in the context
Sports_manga
Vertices connected in pairs by edges
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some
Graph_(discrete_mathematics)
Result from multiplying no factors
diagram given by the discrete category with n objects. An empty product is then given by the limit with respect to the empty category, which is the terminal
Empty_product
Set of characters that share common design features
some argument exists as to whether Transitional fonts exist as a discrete category among serif fonts, Transitional fonts lie somewhere between Old Style
Typeface
Category-theoretic construction
theory. The coproduct in a category C {\displaystyle C} can be defined as the colimit of any functor from a discrete category J {\displaystyle J} into C
Coproduct
Mathematics construct
the comma category ( S ↓ T ) {\displaystyle (S\downarrow T)} , written ( A ↓ B ) {\displaystyle (A\downarrow B)} , is the discrete category whose objects
Comma_category
Approach to public-key cryptography
elliptic-curve protocols, a central hardness assumption is the elliptic curve discrete logarithm problem (ECDLP): given a public base point P {\displaystyle P}
Elliptic-curve_cryptography
Concept in psychology related to attachment
1990). A further constraint is that the coding procedure results in discrete categories rather than continuously distributed dimensions. Not only is this
Strange_situation
reason why categories with this property are called "topological". There are numerous consequences of this property. For example: "Discrete" and "indiscrete"
Category of topological vector spaces
Category_of_topological_vector_spaces
Mathematical function for the probability a given outcome occurs in an experiment
numbers), it is common to distinguish between discrete and continuous random variables. In the discrete case, it is sufficient to specify a probability
Probability_distribution
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
Electrical circuit with active components
can be moved from one place to another. Circuits can be constructed of discrete components connected by individual pieces of wire, but today it is much
Electronic_circuit
Text from Aristotle's Organon
The Categories (Ancient Greek: Κατηγορίαι, romanized: Katēgoriai; Latin: Categoriae or Praedicamenta) is a text from Aristotle's Organon that enumerates
Categories_(Aristotle)
Topics referred to by the same term
Wiktionary, the free dictionary. Digital usually refers to something using discrete digits, often binary digits. Digital bank, a form of financial institution
Digital
Category whose objects are topological spaces and whose morphisms are continuous maps
Topological categories have many properties in common with T o p {\displaystyle \mathbf {Top} } (such as fiber-completeness, discrete and indiscrete
Category of topological spaces
Category_of_topological_spaces
diagnostic practices. Classical views of personality disorder as discrete categories have had benefits for understanding and communicating psychopathology
Classification of personality disorders
Classification_of_personality_disorders
Relationship between two functors abstracting many common constructions
which assigns to a category its set of connected components is left-adjoint to the functor D which assigns to a set the discrete category on that set. Moreover
Adjoint_functors
Mythological son of Odysseus
Telemachus (/təˈlɛməkəs/ tə-LEM-ə-kəs; Ancient Greek: Τηλέμαχος, romanized: Tēlemakhos, lit. 'far-fighter') is the son of Odysseus and Penelope in Greek
Telemachus
1970 manga by Keiko Takemiya
success; it is credited with establishing male–male romance as a discrete category of manga, and launching Takemiya's career as a manga artist in earnest
Sunroom_Nite
discrete categories of objects of C , D {\displaystyle C,D} and the two functors are inclusions. In the case of groups seen as one-object categories,
Premonoidal_category
Simplicial set constructed from the objects and morphisms of a small category
original category C, or about related categories. The notion of nerve is a direct generalization of the classical notion of classifying space of a discrete group;
Nerve_(category_theory)
Scientific theory
has failed to yield consistent support for the existence of such discrete categories of experience. Instead, the empirical evidence suggests that what
Theory_of_constructed_emotion
Problem of finding the best feasible solution
two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization
Optimization_problem
Classification of mental health problems
psychopathology is best characterized by dimensions rather than in discrete categories. Dimensions are defined as continua that reflect individual differences
Hierarchical Taxonomy of Psychopathology
Hierarchical_Taxonomy_of_Psychopathology
Mathematical set formed from two given sets
categorical limit, where the indexing category is discrete. As category of sets can be identified with discrete categories and embedded this way as full subcategory
Cartesian_product
American ritual invocations of religion by government
government can, in a discrete category of cases, acknowledge or refer to the divine without offending the Constitution. This category of "ceremonial deism"
Ceremonial_deism
Pattern of romantic/sexual attraction based on sex/gender
human sexual response looked more like a continuum than two or three discrete categories. Berlin sexologist Magnus Hirschfeld published a scheme in 1896 that
Sexual_orientation
Mathematical concept
compact objects in the category of topological spaces. Instead these are precisely the finite sets endowed with the discrete topology. The link between
Compact_object_(mathematics)
Visual representation of data
be continuous or discrete. Continuous variables capture the idea that measurements can always be made more precisely. While discrete variables have only
Data and information visualization
Data_and_information_visualization
Method of encoding digital data on multiple carrier frequencies
more robust modulation or error coding to those subcarriers. The term discrete multitone modulation (DMT) denotes OFDM-based communication systems that
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Processes through which companies combine or transfer ownership
Megadeals—deals of at least one $1 billion in size—tend to fall into four discrete categories: consolidation, capabilities extension, technology-driven market
Mergers_and_acquisitions
Type of topological space
homeomorphic to the projective limit (in the category of topological spaces) of an inverse system of finite discrete spaces; X {\displaystyle X} is compact
Stone_space
Belief that God and reality are identical
systems of classifying them relying upon one or more spectra or in discrete categories. The philosopher Charles Hartshorne used the term Classical Pantheism
Pantheism
American pharmaceutical company
ravings, the fantastic metaphors, and putting them into discernible, discrete categories that are defined and can be used again extending the realm of what
Mindstate_Design_Labs
Branch of mathematics concerning probability
space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic
Probability_theory
Jewelry used to complement a particular costume
if they are of an unusual design. Costume jewelry is considered a discrete category of fashion accessory and displays many characteristics of a self-contained
Costume_jewelry
In ontology, the highest kinds or genera of entities
theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being, or
Theory_of_categories
Category admitting tensor products
0-sphere (a two-point discrete space) serving as the unit. The category of all endofunctors on a category C is a strict monoidal category with the composition
Monoidal_category
Things made and done for people
of consumables into services is a simplification: these are not discrete categories. Most business theorists see a continuum with pure service at one
Goods_and_services
Python library for data analysis
intervals, thereby allowing continuous measurements to be analyzed as discrete categories. Create example time series data, daily: periods = 30 days = pd.date_range(start='1
Pandas_(software)
Family of algorithms for sampling from discrete probability distributions
the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker. That
Alias_method
Public-key cryptosystem
ElGamal (1985). "A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms" (PDF). IEEE Transactions on Information Theory. 31 (4): 469–472
ElGamal_encryption
Topological space with a distinguished point
pointed set concept is less important; it is anyway the case of a pointed discrete space. Pointed spaces are often taken as a special case of the relative
Pointed_space
Concept in retailing
broken down into discrete groups of similar or related products. These groups are known as product categories (examples of grocery categories might be: tinned
Category_management
Gold clusters, a part of cluster chemistry, describe molecular clusters of gold and some well-defined colloidal particles. Several can described as nanoparticles
Gold_cluster
Random process independent of past history
countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called
Markov_chain
Method of exchanging cryptographic keys
This increases the difficulty for an adversary attempting to compute the discrete logarithm and compromise the shared secret. These two values are chosen
Diffie–Hellman_key_exchange
Field of machine learning
A basic reinforcement learning agent interacts with its environment in discrete time steps. At each time step t, the agent receives the current state S
Reinforcement_learning
Study of abstract machines and automata
considered a branch of mathematical systems theory, studying the behavior of discrete-parameter systems. Early work in automata theory differed from previous
Automata_theory
Array of every physical action and observable emotion associated with humans
that gender and sexual behaviors exist along continuums rather than discrete categories, with significant individual variation in expression and experience
Human_behavior
Discrete probability distribution
distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the
Categorical_distribution
for example, in the case that J {\displaystyle {\mathcal {J}}} is a discrete category with two objects, the diagonal functor C → C × C {\displaystyle {\mathcal
Diagonal_functor
Simplicial object in the category of topological spaces
look like a homotopical version of a category. More precisely, a simplicial set, considered as a simplicial discrete space, satisfies the Segal conditions
Simplicial_space
Automatic grading of educational assignments
classify a large set of textual entities into a small number of discrete categories, corresponding to the possible grades, for example, the numbers 1
Automated_essay_scoring
institutions, and digital spaces. Intelligent cities constitute a discrete category of intelligent environments created by the agglomeration of creativities
URENIO
Recreational drug information website
ravings, the fantastic metaphors, and putting them into discernible, discrete categories that are defined and can be used again extending the realm of what
PsychonautWiki
Mathematical model of the time dependence of a point in space
therefore a discrete set of these in a discrete time interval Δ t {\displaystyle \Delta t} is again a shape of characterization of the full discrete dynamical
Dynamical_system
Traditional Igbo divination system
appear across all four domains rather than being segregated into a discrete category. Beyond the binary structure of individual throws, afa meaning is
Afa_(Igbo_divination)
Statistical analyses that were not specified before the data were seen
addition, a subgroup analysis examines whether findings differ between discrete categories of subjects in the sample. This approach is common in clinical and
Post_hoc_analysis
Category whose objects are measurable spaces and whose morphisms are measurable maps
function between discrete or between indiscrete spaces is measurable, both of these functors give full embeddings of Set into Meas. The category Meas is both
Category_of_measurable_spaces
Concept in abstract algebra
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an
Discrete_valuation_ring
Mathematical category formed by reversing morphisms
equivalence between the category of compact Hausdorff abelian topological groups and the opposite of the category of (discrete) abelian groups. By the
Opposite_category
Algorithm for public-key cryptography
Goldwasser–Micali Naccache–Stern Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa Discrete logarithm BLS Cramer–Shoup DH DSA ECDH X25519 X448 ECDSA EdDSA Ed25519
RSA_cryptosystem
Modern reformulation of the calculus in terms of infinitesimals
employing the methods of category theory, it views all functions as being continuous and incapable of being expressed in terms of discrete entities. As a theory
Smooth_infinitesimal_analysis
Simple polynomial map exhibiting chaotic behavior
The logistic map is a discrete dynamical system defined by the quadratic difference equation It is a recurrence relation and a polynomial mapping of degree 2
Logistic_map
Variable representing a random phenomenon
countably infinite, the random variable is called a discrete random variable and its distribution is a discrete probability distribution, i.e. can be described
Random_variable
Overview of and topical guide to natural language processing
classify a large set of textual entities into a small number of discrete categories, corresponding to the possible grades—for example, the numbers 1
Outline of natural language processing
Outline_of_natural_language_processing
Signal representation
frequency domain. A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform
Frequency_domain
Finest topology making some functions continuous
language of category theory, the final topology construction can be described as follows. Let Y {\displaystyle Y} be a functor from a discrete category J {\displaystyle
Final_topology
DISCRETE CATEGORY
DISCRETE CATEGORY
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DISCRETE CATEGORY
DISCRETE CATEGORY
DISCRETE CATEGORY
DISCRETE CATEGORY
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DISCRETE CATEGORY