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#redirect [[Cycle (graph theory)]] [[Category:Graph theory objects]] ...

...a [[fibration]] to the [[terminal object]] of the [[category (mathematics)|category]]. ...roup]]s. In the context of the theory of [[simplicial set]]s, the fibrant objects are known as '''Kan complexes''' after [[Daniel Kan]]. They are the [[Kan f ...

{{Short description|Category whose only morphisms are the identity morphisms}} ...ics]], in the field of [[category theory]], a '''discrete category''' is a category whose only [[morphism]]s are the [[identity morphism]]s: ...

{{Short description|Philosophical theory}} ...crete'' objects at all, so that even if every possible world contains some objects, there is at least one that contains only [[abstract object]]s.<ref>{{cite ...

...h, for every two objects ''X'' and ''Y'' there is a [[finite sequence]] of objects ...ry]] is constant. In some cases it is convenient to not consider the empty category to be connected. ...

...cription of the product of objects ''within'' the [[Category (mathematics)|category]] <math>\mathcal{C}</math>: a product <math>a \times b</math> is a universa ...the case that <math>\mathcal{J}</math> is a [[discrete category]] with two objects, the diagonal functor <math>\mathcal{C} \rightarrow \mathcal{C} \times \mat ...

...(mathematics)|groups]]. Semigroupoids have applications in the structural theory of semigroups. * a [[Set (mathematics)|set]] of things called ''objects''. ...

{{Short description|1=Overview of and topical guide to category theory}} ...as of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be ...

...nonym for a filtered category). There is a dual notion of '''cofiltered''' category, which will be recalled below. A [[Category (mathematics)|category]] <math>J</math> is '''filtered''' when ...

This is a '''list of [[algebraic number theory]] topics'''. ...opics are basic to the field, either as prototypical examples, or as basic objects of study. ...

{{Short description|Category whose objects and morphisms are inside a bigger category}} ...egory of ''C'' is a category obtained from ''C'' by "removing" some of its objects and arrows. ...

...s of space along with [[relational theory]] and the [[Kantianism|Kantian]] theory.<ref name=":0">{{Cite book|title=Governance Reform in Africa: International ...ependent of other things.<ref name=":0" /> The Newtonian arguments of this theory, particularly those concerned with the [[Ontology|ontological]] status of s ...

{{Short description|Category whose objects are small categories and whose morphisms are functors}} ...functor]]s between categories. '''Cat''' may actually be regarded as a [[2-category]] with [[natural transformation]]s serving as [[2-morphism]]s. ...

===Group theory=== ** [[Category of abelian groups]] (Ab), has abelian groups as objects and group homomorphisms as morphisms ...

{{Short description|Product of two categories, in category theory}} ...uct of categories|the operation on objects of a category|Product (category theory)}} ...

...]]. Outside that field, it has been influential particularly on [[category theory]] and [[categorical logic]]. ...t of view treats not [[object (category theory)|objects]] ''X'' of a given category ''C'', but [[morphism]]s ...

...ogy-local theory, in the sense of [[Bousfield localization]] in [[homotopy theory]]. * [[Derived category]] ...

...ergeometry]], and [[supergravity]], namely in the context of [[superstring theory]]. [[Category:Mathematical physics]] ...

{{Short description|Category of non-empty finite ordinals and order-preserving maps}} ...ap]]s. It is used to define [[simplicial set|simplicial]] and cosimplicial objects. ...

...s]], a '''closed category''' is a special kind of [[category (mathematics)|category]]. ...t of) morphisms from one object to another can be seen as lying inside the category. This is the ''internal hom'' [''x'', ''y'']. ...