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Cell population in developmental biology
An equivalence group is a set of unspecified cells that have the same developmental potential or ability to adopt various fates. Our[who?] current understanding
Equivalence_group
Mathematical concept
a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S {\displaystyle S} into equivalence classes. These
Equivalence_class
Mathematical concept for comparing objects
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments
Equivalence_relation
Tool used to draw statistical inferences from observed data
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined
Equivalence_test
cycles modulo rational equivalence form the classical group of divisors modulo linear equivalence. All cycles modulo rational equivalence form the Chow ring
Adequate_equivalence_relation
Logical fallacy of inconsistency
A false equivalence or false equivalency is an informal fallacy in which an equivalence is drawn between two subjects based on flawed, faulty, or false
False_equivalence
Progenitor cell in annelid development
specified from two separate but identical precursors, which form an equivalence group. These two precursor cells are termed O/P cells for their ability
Teloblast
related areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation E with countable classes, that
Hyperfinite equivalence relation
Hyperfinite_equivalence_relation
Group whose operation is a composition of braids
braid group on n strands (denoted B n {\displaystyle B_{n}} ), also known as the Artin braid group, is the group whose elements are equivalence classes
Braid_group
automorphic equivalence, and regular equivalence. There is a hierarchy of the three equivalence concepts: any set of structural equivalences are also automorphic
Similarity_(network_science)
Abstract mathematics relationship
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories
Equivalence_of_categories
Group in algebraic geometry
geometry, the Néron–Severi group of a variety is the group of divisors modulo algebraic equivalence; in other words it is the group of components of the Picard
Néron–Severi_group
Pharmaceutical equivalent to a brand-name product
divides them into therapeutic equivalence groups. For example, as of 2006, diltiazem hydrochloride had four equivalence groups, all using the same active
Generic_drug
Function between two metric spaces that only respects their large-scale geometry
behaves like an equivalence relation on the class of metric spaces. The concept of quasi-isometry is especially important in geometric group theory, following
Quasi-isometry
Equivalence relation in algebra
congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible
Congruence_relation
Enucleate cell Enzyme Epigenetics Episome Epistasis Equational division Equivalence group Erythrocytes Escherichia coli Ethics Ethidium Euchromatin Eugenics
Index_of_genetics_articles
Topological space construction
mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient
Quotient_space_(topology)
Aspect of the Unicode standard
Unicode equivalence is the specification by the Unicode character encoding standard that some sequences of code points represent essentially the same
Unicode_equivalence
Hypothesis that inertial and gravitational masses are equivalent
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form
Equivalence_principle
In mathematics, a weak equivalence is a notion from homotopy theory that in some sense identifies objects that have the same "shape". This notion is formalized
Weak equivalence (homotopy theory)
Weak_equivalence_(homotopy_theory)
Continuous deformation between two continuous functions
states. Fiber-homotopy equivalence (relative version of a homotopy equivalence) Homeotopy Homotopy type theory Mapping class group Poincaré conjecture Regular
Homotopy
Description of linearly ordered groups
\mathbb {R} } is the additive group of real numbers (with its standard order), Ω is the set of Archimedean equivalence classes of G, and R Ω {\displaystyle
Hahn_embedding_theorem
Differential geometry technique
In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up
Cartan's_equivalence_method
Equivalence relation on rings
In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings
Morita_equivalence
{\operatorname {Hom} }}(X,Y).} A simplicial homotopy is in general not an equivalence relation. However, if Hom _ ( X , Y ) {\displaystyle {\underline {\operatorname
Simplicial_homotopy
In group theory, equivalence class under the relation of conjugation
{\displaystyle g} in the group such that b = g a g − 1 . {\displaystyle b=gag^{-1}.} This is an equivalence relation whose equivalence classes are called conjugacy
Conjugacy_class
(Section 2, English translation) Let X be a topological space. Consider the equivalence relation on continuous paths in X in which two continuous paths are equivalent
Fundamental_groupoid
Equivalence relation between map germs
mathematics, A {\displaystyle {\mathcal {A}}} -equivalence, sometimes called right-left equivalence, is an equivalence relation between map germs. Let M {\displaystyle
A-equivalence
Set of mathematical functions concerning algebraic group isomorphism
compositions of regular Nielsen transformations. The dihedral group of order 10 has two Nielsen equivalence classes of generating sets of size 2. Letting x be an
Nielsen_transformation
Mathematical statement of uniqueness, except for an equivalent structure
Two mathematical objects a and b are called "equal up to an equivalence relation R" if a and b are related by R, or, in notation, if aRb holds. Since
Up_to
Equivalence between the categories of chain complexes and simplicial abelian groups
that there is an equivalence between the category of (nonnegatively graded) chain complexes and the category of simplicial abelian groups. Moreover, under
Dold–Kan_correspondence
functional equivalence (or functional redundancy) is the ecological phenomenon that multiple species representing a variety of taxonomic groups can share
Functional equivalence (ecology)
Functional_equivalence_(ecology)
fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence (namely, homotopy equivalence) should
Borel_conjecture
In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark)
Naimark_equivalence
Assessment of particular interventions
and control groups allows for making the assumption of continuing equivalence. Group comparisons that have not been formed through randomization are known
Impact_evaluation
Group obtained by aggregating similar elements of a larger group
known as group theory, a quotient group or factor group is a group obtained by aggregating similar elements of a larger group using an equivalence relation
Quotient_group
Process involved in cell fate commitment
essentially interchangeable, thus establishing an equivalence group. The developmental equivalence of these cells is usually established via transplantation
Cell_fate_determination
a block system. The corresponding equivalence relation is the smallest G {\displaystyle G} -invariant equivalence on X {\displaystyle X} such that the
Block (permutation group theory)
Block_(permutation_group_theory)
the equivalence classes form a group, called the fundamental group of G and written π1G. (Note that even for a strict 2-group, the fundamental group will
2-group
Mathematical group
induced action of the Galois group G = Gal ( K / k ) {\displaystyle G=\operatorname {Gal} (K/k)} on the set of equivalence classes of valuations such
Galois_group
Mathematical group of the homotopy classes of loops in a topological space
field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained
Fundamental_group
Theorem in category theory
End Exponential Functor Adjoint functors Conservative Derived Diagonal Equivalence of categories Essentially surjective Exact Full and faithful Isomorphism
Lawvere's_fixed-point_theorem
is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on
Whitehead's_algorithm
Relationship between two functors abstracting many common constructions
two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship
Adjoint_functors
Construction in combinatorial group theory
G. The Schreier graph encodes the abstract structure of the group modulo an equivalence relation formed by the cosets of the subgroup. The graph is named
Schreier_coset_graph
Provider of qualifications in England, Wales and Northern Ireland
provide a particularly significant route to higher education for specific groups, with almost half students entering university with a BTEC, alongside large
Business and Technology Education Council
Business_and_Technology_Education_Council
Motorsport regulation for cars
with a 1.4 equivalence factor applied for forced induction engines. Each class had weight and wheel size limits. Notable classes for Group B were the
Group_B
Reflexive and transitive binary relation
{\displaystyle -24} , ..., but no least one). Preorders are closely related to equivalence relations and (non-strict) partial orders. Both of these are special
Preorder
General theory of mathematical structures
situation is called equivalence of categories, which is given by appropriate functors between two categories. Categorical equivalence has found numerous
Category_theory
Mathematical category with weak equivalences, fibrations and cofibrations
category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certain axioms relating
Model_category
Embedding of categories into functor categories
object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms)
Yoneda_lemma
Transformations induced by a mathematical group
properties of a group guarantee that the set of orbits of (points x in) X under the action of G form a partition of X. The associated equivalence relation is
Group_action
Structure in algebraic geometry
groups of varieties. The generalization happens in more than one direction, since motives can be considered with respect to more types of equivalence
Motive_(algebraic_geometry)
Group of rotations in 3 dimensions
in the cases under consideration. The elements of L2(S2) are actually equivalence classes of functions. two functions are declared equivalent if they differ
3D_rotation_group
Type of informal fallacy
Undistributed middle Informal Equivocation Equivocation False equivalence False attribution Moral equivalence Conflation Quoting out of context Loki's Wager No true
Motte-and-bailey_fallacy
(January 2016). "The Historical Loss Scale: Longitudinal Measurement Equivalence and Prospective Links to Anxiety Among North American Indigenous Adolescents"
Indigenous peoples of the Americas
Indigenous_peoples_of_the_Americas
gene (called a proneural cluster) can be thought of as cells of an equivalence group. Within a proneural cluster, the cells compete with each other, such
Proneural_genes
Monoidal category
bounding monodromy groups. The Geometric Satake equivalence establishes an equivalence between representations of the Langlands dual group L G {\displaystyle
Tannakian_formalism
In mathematics, invertible homomorphism
relation that two mathematical objects are isomorphic is an equivalence relation. An equivalence class given by isomorphisms is commonly called an isomorphism
Isomorphism
Psychological bias towards favoring members of one's in-group
In-group favoritism, sometimes known as in-group–out-group bias, in-group bias, intergroup bias, or in-group preference, is a pattern of favoring members
In-group_favoritism
Group in group theory and physics
with given action of the central Lie algebra element z, up to a unitary equivalence: the nontrivial elements of the algebra are all equivalent to the usual
Heisenberg_group
Mathematical ways to group elements of a set
exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped
Partition_of_a_set
Social networking service owned by Meta Platforms
California Consumer Privacy Act. Some, such as Meghan McCain, have drawn an equivalence between the use of data by Cambridge Analytica and the Barack Obama's
Classification of a two-dimensional repetitive pattern
significant, not the colour): On the right-hand side diagrams, different equivalence classes of symmetry elements are colored (and rotated) differently. The
Wallpaper_group
Theorem in homotopy theory
complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark
Whitehead_theorem
Form of incorrect argument and informal fallacy
non-representative statements from members of an opposing group and parading these as evidence of that entire group's incompetence or irrationality. A steel man argument
Straw_man
Pictorial computational technique in quantum chemistry
ISBN 978-0-08-087258-2. P. Cvitanović (2008). Group Theory - Birdtracks, Lie's, and Exceptional Groups. Princeton, NJ: Princeton Univ. Press. ISBN 978-0-691-11836-9
Angular momentum diagrams (quantum mechanics)
Angular_momentum_diagrams_(quantum_mechanics)
Smallest monoid that recognizes a formal language
syntactic quotient induces an equivalence relation on M {\displaystyle M} , called the syntactic relation, or syntactic equivalence (induced by S {\displaystyle
Syntactic_monoid
Projective line over the real numbers
all equivalence classes. Each equivalence class is considered as a single point, or, in other words, a point is defined as being an equivalence class
Real_projective_line
Decomposition of an algebraic structure
unique up to equivalence. Groups with a set of operators generalize group actions and ring actions on a group. A unified approach to both groups and modules
Composition_series
simply-connected manifolds, the Whitehead group vanishes, and thus homotopy equivalences and simple homotopy equivalences are the same. The applications are
Whitehead_torsion
Statistical property of measurement
measurement equivalence is a statistical property of measurement that indicates that the same construct is being measured across some specified groups. For example
Measurement_invariance
Well-quasi-ordering of finite trees
algebra topics Completeness Connected Covering Dense Directed (Partial) Equivalence Foundational Heyting algebra Homogeneous Idempotent Lattice Bounded Complemented
Kruskal's_tree_theorem
Mathematical symbol of equality
conditional statements ("if x = 2, then ..."), or to express a universal equivalence ("(x + 1)2 = x2 + 2x + 1"). The first important computer programming
Equals_sign
Equation that is satisfied for all values of the variables
{\displaystyle \theta =0,} but false when θ = 2 {\displaystyle \theta =2} . Another group of trigonometric identities concerns the so-called addition/subtraction
Identity_(mathematics)
Most general completion of a commutative square given two morphisms with same codomain
commutative rings above, one can show that all pullbacks exist in the category of groups and in the category of modules over some fixed ring. In the category of
Pullback_(category_theory)
Generalization of a category
respect to weak equivalences is a presentable ∞-category and conversely, each presentable ∞-category is of such form, up to equivalence. An (∞, 1)-category
Quasi-category
Aspect of category theory
(or coequaliser) is a generalization of the quotient of a set by an equivalence relation to objects in an arbitrary category. It is the categorical construction
Coequalizer
Injective homomorphism
monomorphism need not be left-invertible. For example, in the category Group of all groups and group homomorphisms among them, if H is a subgroup of G then the inclusion
Monomorphism
age groups. To calculate equivalised income using the modified OECD equivalence scale, each member of the household is first given an equivalence value:
Equivalisation
Smallest cardinality of a generating set for a group
Rank of an abelian group Prüfer rank Grushko theorem Free group Nielsen equivalence D. J. S. Robinson. A course in the theory of groups, 2nd edn, Graduate
Rank_of_a_group
Mathematical theorem
Wayback Machine for equivalence of (C) and (C′) [3] for a proof of (B′)⇒(A). Bourbaki, Nicolas, Éléments de mathématiques : Groupes et algèbres de Lie
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Operation in group theory
given groups by using the Cartesian product as a set and a particular multiplication operation. As with direct products, there is a natural equivalence between
Semidirect_product
Sovereign countries that are bound by EU laws, rights, and obligations
and the Treaty on the Functioning of the European Union - Tables of equivalences Archived 27 December 2017 at the Wayback Machine, Eur-Lex As outlined
Member state of the European Union
Member_state_of_the_European_Union
Topological group that is in a certain sense assembled from a system of finite groups
profinite group is a topological group that is in a certain sense assembled from a system of finite groups. The idea of using a profinite group is to provide
Profinite_group
Checking software against expectations
supposed to do, not how it does it. Black-box testing methods include: equivalence partitioning, boundary value analysis, all-pairs testing, state transition
Software_testing
Equivalence relation of groups
G} , denoted Comm ( G ) {\displaystyle {\text{Comm}}(G)} , is the group of equivalence classes of isomorphisms ϕ : H → K {\displaystyle \phi :H\to K} ,
Commensurability (group theory)
Commensurability_(group_theory)
Quotient of special unitary group by its center
where I is the identity matrix. Thus, elements of PU(n) correspond to equivalence classes of unitary matrices under multiplication by a constant phase
Projective_unitary_group
Type of category in category theory
functions as morphisms, is also Cartesian closed for the same reason. If G is a group, then the category of all G-sets is Cartesian closed. If Y and Z are two
Cartesian_closed_category
Hypothesis about quantum and statistical mechanics
Liquids" by Matthew P. A. Fisher, UCSB, KITP Conference: From the Renormalization Group to Quantum Gravity Celebrating the science of Joe Polchinski
Eigenstate thermalization hypothesis
Eigenstate_thermalization_hypothesis
Fallacy of assumption of causation based on sequence of events
Undistributed middle Informal Equivocation Equivocation False equivalence False attribution Moral equivalence Conflation Quoting out of context Loki's Wager No true
Post_hoc_ergo_propter_hoc
Refutation of a logical fallacy
Bradford Hill criteria, also known as Hill's criteria for causation, are a group of nine principles that can be useful in considering the epidemiologic evidence
Correlation does not imply causation
Correlation_does_not_imply_causation
Mathematical group occurring in algebraic geometry and the theory of complex manifolds
algebraic equivalence classes of divisors on V; that is, using a stronger, non-linear equivalence relation in place of linear equivalence of divisors
Picard_group
the analogous statement for the group CH 2 ( S ) {\displaystyle \operatorname {CH} ^{2}(S)} of rational equivalence classes of codimension two cycles
Algebraic_cycle
Specification of a mathematical group by generators and relations
removing a consecutive copy of a relator. The group elements are the equivalence classes, and the group operation is concatenation. This point of view
Presentation_of_a_group
Tools for studying groups based on techniques from algebraic topology
natural equivalence relation). More generally, if the action of G on M is nontrivial, H2(G,M) classifies the isomorphism classes of all group extensions
Group_cohomology
Topics referred to by the same term
class/category equivalence (for labeling) Group V - group/category equivalence (for labeling) Category 5 (disambiguation) - Roman/Arabic numbering equivalence This
Category_V
Equivalence is a term applied by the Uruguay Round Agreement on the Application of Sanitary and Phytosanitary Measures. World Trade Organization (WTO)
Equivalence_(trade)
Number in {..., –2, –1, 0, 1, 2, ...}
are independent of the choice of representatives of the equivalence classes. Every equivalence class has a unique member that is of the form (n,0) or (0
Integer
President of the United States (2017–2021; since 2025)
"very fine people on both sides", were criticized as implying a moral equivalence between the white supremacist demonstrators and the counter-protesters
Donald_Trump
EQUIVALENCE GROUP
EQUIVALENCE GROUP
Girl/Female
English
Titled. Feminine equivalent of Count.
Boy/Male
Muslim American Biblical English Hebrew
The Biblical Adam is the English language equivalent.
Boy/Male
Muslim
The Biblical Elijah is the English language equivalent.
Boy/Male
Muslim
The Biblical Elijah is the English language equivalent.
Boy/Male
Muslim
The Biblical Adam is the English language equivalent.
Boy/Male
Muslim
The Biblical Ezekiel is the English language equivalent.
Boy/Male
Muslim
The Biblical Jacob is the English language equivalent.
Boy/Male
Muslim
The Biblical Jacob is the English language equivalent.
Girl/Female
Indian, Sanskrit
Equivalent to a God
Boy/Male
Muslim
The Biblical Elijah is the English language equivalent.
Boy/Male
Muslim
The Biblical Jethro is the English language equivalent.
Girl/Female
Hawaiian American Latin Slavic Spanish
Equivalent of English Lara: famous;cheerful.
Boy/Male
Muslim
The Biblical Areran is the English language equivalent.
Boy/Male
Muslim
The Biblical Abel is the English language equivalent.
Boy/Male
Indian, Sanskrit
Equivalent to Ten Heavens; Very Powerful
Boy/Male
Muslim
Ezekiel (English language equivalent).
Boy/Male
Scandinavian
Royalty title approximately equivalent to the English Earl.
Girl/Female
Hawaiian
Sound. Also the Hawaiian equivalent of Sandy.
Girl/Female
American, British, English
Feminine Equivalent of Count; Titled
Boy/Male
Muslim
The Biblical Ezra is the English language equivalent.
EQUIVALENCE GROUP
EQUIVALENCE GROUP
EQUIVALENCE GROUP
EQUIVALENCE GROUP
EQUIVALENCE GROUP
EQUIVALENCE GROUP
EQUIVALENCE GROUP