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Aspect of category theory
A coequalizer is the colimit of a diagram consisting of two objects X and Y and two parallel morphisms f, g : X → Y. More explicitly, a coequalizer of
Coequalizer
Theorem in category theory
split coequalizer sequence in D is itself a coequalizer sequence in C. In different words, U creates (preserves and reflects) U-split coequalizer sequences
Beck's_monadicity_theorem
Most general completion of a commutative square given two morphisms with same domain
are coequalizers and coproducts; Pushouts can be constructed from coproducts and coequalizers, as described below (the pushout is the coequalizer of the
Pushout_(category_theory)
Mathematical category with finite limits and coequalizers
complete. If f : X → Y is a morphism in C, and is a pullback, then the coequalizer of p0, p1 exists. The pair (p0, p1) is called the kernel pair of f. Being
Regular_category
Surjective homomorphism
be regular if it is a coequalizer of some pair of parallel morphisms. An epimorphism f is said to be strict if it is a coequalizer of every pair of morphisms
Epimorphism
Quotient space of a codomain of a linear map by the map's image
zero morphisms. The cokernel of a morphism f : X → Y is defined as the coequalizer of f and the zero morphism 0XY : X → Y. Explicitly, this means the following
Cokernel
President of the United States from 1861 to 1865
Hampton Roads. Lincoln refused to negotiate with the Confederacy as a coequal, and the only agreement reached at the meeting concerned the exchange of
Abraham_Lincoln
Language avoiding bias towards a sex or social gender
gender-specific to refer to roles or professions, formation of phrases in a coequal manner, and discontinuing the collective use of male or female terms. For
Gender-neutral_language
Type of crime family
closely enough with the Five Families that it appears to be a peer or near coequal of the families. Various criminal organizations have been deemed the "Sixth
Sixth_Family
Mathematical category
relation on the set Hom(Y, X). Since C has colimits we may form the coequalizer of the two maps R → X; call this X/R. The equivalence relation is "effective"
Topos
Generalized object in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Product_(category_theory)
Mormon. Barb becomes fed up with interning. She claims that women are coequal with men in their relationship to God and believes herself to be a priesthood
List_of_Big_Love_episodes
U.S. state
codifying segregation and racism. Alabama's government is divided into three coequal branches. The legislative branch is the Alabama Legislature, a bicameral
Alabama
establishing the Consulate (10 November 1799 – 18 May 1804). While initially a coequal of the other Consuls, Napoleon quickly set himself up as "First Consul
List of prime ministers of France
List_of_prime_ministers_of_France
Topics referred to by the same term
(disambiguation) Trinity, the Christian doctrine of one God existing in three coequal, coeternal, consubstantial divine persons This disambiguation page lists
Three_body
Type of category in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Cartesian_closed_category
head of government retains executive power. The two co-princes serve coequally with limited powers that do not include an individual veto over government
Politics_of_Andorra
Object in category theory
that z and s form a coproduct diagram for NNOs; also, !N : N → 1 is a coequalizer of s and 1N, i.e., every pair of global elements of N are connected by
Natural_numbers_object
U.S. state
executive branch, while legislative authority vests in a separate but coequal legislature. Meanwhile, judicial power is constitutionally guaranteed to
Massachusetts
American public research university
major institution in its own right. In 1951, UCLA was formally elevated to coequal status with UC Berkeley, with both institutions headed by chancellors who
University of California, Los Angeles
University_of_California,_Los_Angeles
Supreme legal document of India since 1950
representatives in the Council of States. On most topics the Rajya Sabha is coequal with the lower house or Lok Sabha, and its consent is required for a bill
Constitution_of_India
Category whose objects are measurable spaces and whose morphisms are measurable maps
set-theoretic equalizer. Dually, the coequalizer is given by placing the quotient sigma-algebra on the set-theoretic coequalizer. Direct limits and inverse limits
Category_of_measurable_spaces
Structure of the U.S. Space Force
space deltas, and squadrons. The Space Force is organized as one of two coequal military service branches within the Department of the Air Force, the other
Structure of the United States Space Force
Structure_of_the_United_States_Space_Force
Highest court of jurisdiction in the U.S
Marshall sought to do away with this practice to help build the Court into a coequal branch. Suddath, Claire (December 19, 2008). "A Brief History of Impeachment"
Supreme Court of the United States
Supreme_Court_of_the_United_States
German royal family and dynasty
exclusive primogeniture in the male line as well as marriage restrictions on coequal level. In 1867 the House created the Royal Dukedom of Urach for a younger
House_of_Württemberg
Government in British America
unlimited, while the American position was that colonial legislatures were coequal with Parliament and outside of its jurisdiction. As the revolution progressed
Colonial government in the Thirteen Colonies
Colonial_government_in_the_Thirteen_Colonies
General theory of mathematical structures
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Category_theory
the trading posts of VOC within the Indian subcontinent). Bharat is a coequal name of India, as set down in Article 1 of the Constitution, adopted in
Names_of_India
Fossilised organism
The diameter of the bodies and the spaces between each one is almost coequal, and the number of bodies within a given series decreases when they grow
Horodyskia
Military department for the Navy and Marine Corps, U.S. Department of Defense
Coast Guard (USCG). These branches remain at all times independent and coequal service branches within the DON. It is led by the secretary of the Navy
United States Department of the Navy
United_States_Department_of_the_Navy
Early Christian and Jewish religious systems
classic Gnostic movements. Radical dualism, or absolute dualism, posits two coequal divine forces, while in mitigated dualism one of the two principles is
Gnosticism
Category of non-empty finite ordinals and order-preserving maps
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Simplex_category
Higher categorical generalization of a topos
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
∞-topos
Court with jurisdiction over disputes with some connection to a U.S. state
implied and others later developed the idea that American judges were coequal to legislatures and executives in their responsibility to carry out the
State_court_(United_States)
American actor and military officer (1908–1997)
personality of the alter ego." Bingham has described him as having "two coequal personas; the earnest idealist, the nostalgic figure of the homespun boy
James_Stewart
Generalization of equivalence classes to scheme theory
equivalence relation f : R → X × X {\displaystyle f:R\to X\times X} is a coequalizer for the pair of maps R → f X × X → pr i X , i = 1 , 2 , {\displaystyle
Quotient by an equivalence relation
Quotient_by_an_equivalence_relation
Maritime service branch of the U.S. military
policy. The Navy is part of the Department of the Navy, alongside the coequal United States Marine Corps, and which is headed by the secretary of the
United_States_Navy
Combined military forces of the United States
Department of the Air Force) are civilian led entities that oversee the coequal military service branches organized within each department. The military
United_States_Armed_Forces
Mathematical concept
{\displaystyle \mathbf {C} } is small, then the coend can be described as the coequalizer in the diagram ∫ c S ( c , c ) ← ∐ c ∈ C S ( c , c ) ⇇ ∐ c → c ′ S (
End_(category_theory)
Category-theoretic construction
the product, this functor is covariant. Product Limits and colimits Coequalizer Direct limit Qiaochu Yuan (June 23, 2012). "Banach spaces (and Lawvere
Coproduct
Space service branch of the U.S. military
part of the Department of the Air Force alongside the U.S. Air Force, a coequal service. The Department of the Air Force is headed by the civilian secretary
United_States_Space_Force
Siege of Rome during the Gothic War
in advance of the Lazic War (541–562). Belisarius was replaced by three coequal commanders, whose rivalry and corruption led to indiscipline and plundering
Sack_of_Rome_(546)
American social-political scandal
finances, especially in a frontier economy where kinship networks were coequal with business relationships, were concerning to his in-laws. Further to
Robards–Donelson–Jackson relationship controversy
Robards–Donelson–Jackson_relationship_controversy
In mathematics, invertible homomorphism
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Isomorphism
Category whose objects are topological spaces and whose morphisms are continuous maps
set-theoretic equalizer. Dually, the coequalizer is given by placing the quotient topology on the set-theoretic coequalizer. Direct limits and inverse limits
Category of topological spaces
Category_of_topological_spaces
1993 UK local government election
year of the Council, with the three main party groups being briefed on a coequal basis. Following a by-election gain by the Liberal Democrats from the Conservatives
1993 Wiltshire County Council election
1993_Wiltshire_County_Council_election
Category whose objects are rings and whose morphisms are ring homomorphisms
equalizer (the equalizer of two ring homomorphisms is always a subring). The coequalizer of two ring homomorphisms f and g from R to S is the quotient of S by
Category_of_rings
but destined to be Alexander's successor, defined the co-eternity and coequality of the Father and the Son, using the now famous term homoousios to express
Diversity in early Christian theology
Diversity_in_early_Christian_theology
Indexed collection of objects and morphisms in a category
Y)} is then a quiver; its limit is an equalizer, and its colimit is a coequalizer. If J is a poset category, then a diagram of type J is a family of objects
Diagram_(category_theory)
Overview of and topical guide to category theory
theory)/fiber product Inverse limit Pro-finite group Colimit Coproduct Coequalizer Cokernel Pushout (category theory) Direct limit Biproduct Direct sum
Outline_of_category_theory
Constructs a fiber bundle from a base space, fiber and a set of transition functions
tij are all smooth. Existence is proven constructively by the standard coequalizer construction in category theory. Take the disjoint union of the product
Fiber bundle construction theorem
Fiber_bundle_construction_theorem
Embedding of categories into functor categories
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Yoneda_lemma
Western half of the Roman Empire (395–476)
imperial court. Particularly from AD 395 to 476, there were separate, coequal courts dividing the governance of the empire into western and eastern provinces
Western_Roman_Empire
Object within another object of the same category
class of "regular epimorphisms" (morphisms which can be expressed as a coequalizer of two morphisms) This definition corresponds to the ordinary understanding
Subobject
Structure of the Bangladesh Army
command, 1 logistics command and 10 area commands consigned with their coequal divisions. The training command is also the doctrine body of the army and
List of formations of the Bangladesh Army
List_of_formations_of_the_Bangladesh_Army
Assemblies of the Roman people
republic. The plebeian council, on the other hand, was formed and became coequal with the other assemblies over the course of the Conflict of the Orders
Roman_assemblies
Mapping between categories
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Functor
Theorem in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Lawvere's_fixed-point_theorem
Legendary author of the Hermetica
periods. The renowned scribe Amenhotep and a wise man named Teôs were coequal deities of wisdom, science, and medicine; and, thus, they were placed alongside
Hermes_Trismegistus
category with one object whose morphisms are the elements of R. coequalizer The coequalizer of a pair of morphisms f , g : A → B {\displaystyle f,g:A\to
Glossary_of_category_theory
Fiber bundle
principal bundle P {\displaystyle P} . In category theory, this is the coequalizer construction. There are two continuous maps P × G × F → P × F {\displaystyle
Associated_bundle
High-ranking church official
Empire (Reichsfürst), holding a direct vote in the Imperial Diet assembly coequal to an actual Prince-abbot, as in each case treated below. The monastery
Prince-provost
any, is a group object called the inertia group of the groupoid. The coequalizer of the same diagram, if any, is the quotient of the groupoid. Each groupoid
Groupoid_object
Empress regnant of China from 690 to 705
governmental offices and banners. Wu elevated Luoyang's status, making it a coequal capital. At her nephew Wu Chengsi's suggestion, she expanded the shrine
Wu_Zetian
Three-volume work by Karl Marx, 1867–1894
capitalist mode of production. It presents capital, land, and labour as coequal, independent sources of wealth, obscuring the fact that profit and rent
Das_Kapital
Mosque in Abuja, Federal Capital Territory, Nigeria
Imams who were hitherto addressed as Deputy Chief Imams were appointed as coequal Imams of National Mosque to assist the Murshid. They are Prof. Ibrahim
Abuja_National_Mosque
Government ministry of Japan
branches were directly responsible to the director general and functioned as coequal bodies with the Joint Staff Council and the staff offices. This structure
Ministry_of_Defense_(Japan)
Elements taken to zero by a homomorphism
{\displaystyle \pi } from the category to its quotient category acting as the coequalizer of the two projection functors. A functor F : C → D {\displaystyle F:{\mathbf
Kernel_(algebra)
Category theory concept
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Overcategory
Military political officer in Communist countries
commissar was a high-ranking functionary at a military headquarters who held coequal rank and authority with the military commander of the unit. The Bolshevik
Commissar
Applications of category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Applied_category_theory
Type of administrative subdivision in Francophone countries
These are normally subunits of a department and may either contain or be coequal with communes (towns). In Mali the arrondissement is a subunit of a cercle
Arrondissement
American federal judge (born 1963)
Neomi Rao's majority opinion, a "judicial intrusion into the autonomy of a coequal department." On December 22, 2025, Boasberg ruled that 137 men deported
James_Boasberg
1986 studio album by Billy Joel
literal: failed wise guy in 'Big Man on Mulberry Street,' Ray Charles's coequal on 'Baby Grand.' And even at his most rockin' he's seventy-five years retro
The_Bridge_(Billy_Joel_album)
Relation of categories in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Isomorphism_of_categories
Mathematical concept
diagrams from discrete categories. Coequalizers are colimits of a parallel pair of morphisms. Cokernels are coequalizers of a morphism and a parallel zero
Limit_(category_theory)
Topological construct
map), glue the two trivial bundles together via f. Formally, it is the coequalizer of the inclusions S n − 1 × F → D + n × F ∐ D − n × F {\displaystyle
Clutching_construction
Category admitting tensor products
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Monoidal_category
Christian statement of belief focused on Trinitarian doctrine and Christology
or less than another. But the whole three Persons are coeternal, and coequal. So that in all things, as aforesaid; the Unity in Trinity, and the Trinity
Athanasian_Creed
Deliberative assembly that makes laws
legislature in a presidential system is considered an independent and coequal branch of government along with both the judiciary and the executive. Nevertheless
Legislature
Construction in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Inverse_limit
Map (arrow) between two objects of a category
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Morphism
Bi-universal property in category theory
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Zero_morphism
Head of state of Austria
provisional constitution. Additionally, the National Assembly appointed three coequal chairmen, one of them being Karl Seitz, and established a State Council
President_of_Austria
Two fundamental and often opposing concepts
collaborate rather than compete, and they contribute to the creation in a coequal way. In many other instances the two beings are not of the same importance
Dualism_in_cosmology
Imperial title in the Roman and Byzantine Empires
system of rule by two senior emperors and two junior colleagues. The two coequal senior emperors were styled identically to previous Emperors, as augustus
Caesar_(title)
Concept in mathematics
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Tensor–hom_adjunction
Government practice of having three legislative chambers
Lower Chamber, was coequal to the upper chamber. Its members were elected by the electorate. Efri deild, the Upper Chamber, was coequal to the lower chamber
Tricameralism
First-level administrative division in various countries
nine of the 85 federal subjects are called krais (Russian: края, kraya), coequal to oblasts. The toponym Krajina refers to several historical regions in
Kraj
[interfering] with the peaceful transition of power, and [imperiling] a coequal branch of government" Adopted by the House by a vote of 232–197 on January
List of impeachment resolutions introduced against Donald Trump
List_of_impeachment_resolutions_introduced_against_Donald_Trump
Dependency of England and then of Great Britain (1542–1800)
of England became "King of Ireland", theoretically elevating Ireland to coequal status with England, as a kingdom in personal union. There followed an
Kingdom_of_Ireland
Study of Christian belief and practice
as Father), is the Son of God. He is considered (by Trinitarians) to be coequal with the Father and Holy Spirit. He is all God and all human: the Son of
Christian_theology
Federal building in Washington, D.C.
keeping with the importance and dignity of the Court and the Judiciary as a coequal, independent branch of the United States Government, and as a symbol of
United States Supreme Court Building
United_States_Supreme_Court_Building
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Stable_∞-category
Public university system in California
when UCLA became the first UC site outside of Berkeley to achieve de jure coequal status with the Berkeley campus. That month, the regents approved a reorganization
University_of_California
Relationship between two functors abstracting many common constructions
vector spaces and modules are left adjoints. Coproducts, pushouts, coequalizers, and cokernels are all examples of the categorical notion of a colimit
Adjoint_functors
Mathematical object that generalizes the standard notions of sets and functions
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Category_(mathematics)
head of government retains executive power. The two co-princes serve coequally with limited powers that do not include veto over government acts. Both
Executive_Council_of_Andorra
Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories Sets
Diagonal_functor
Topics referred to by the same term
epimorphisms, monomorphisms (resp. epimorphisms) which equalize (resp. coequalize) some parallel pair of morphisms Regular numbers, numbers which evenly
Regular
COEQUALIZER
COEQUALIZER
COEQUALIZER
COEQUALIZER
Girl/Female
Tamil
Of videhas, Princess of videhas
Girl/Female
Hindu
Name of a Goddess, Contented, Satisfied, Pleased
Female
French
French form of Latin Igerna, IGERNE means "maiden, virgin."Â
Girl/Female
Muslim
Precious thing, Gem, Princess, Refined, Pure, Exquisite
Boy/Male
English
Diminutives of any masculine or feminine name begining with Christ-, for example Christahel,...
Boy/Male
British, English, Italian, Malaysian
Mother
Surname or Lastname
English
English : habitational name from Keele in Staffordshire, named from Old English c̄ ‘cows’ + hyll ‘hill’, or from East and West Keal in Lincolnshire, which are named from Old Norse kjǫlr ‘ridge’.Irish : reduced form of McKeel.Swiss German : probably a variant of Kehl 2.Americanized spelling of German Kühl (see Kuhl) or Kiehl, Kiel (see Kiel).
Surname or Lastname
English
English : variant of Woodham.
Boy/Male
Hindu, Indian, Tamil
Charity of Money
Male
Ukrainian
, God's gift.
COEQUALIZER
COEQUALIZER
COEQUALIZER
COEQUALIZER
COEQUALIZER