A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
(Co)Slice Category(Co)Slice Functor+00-category0-cell11-category1-cell1-functors2-Category2-category2-cell2-functor2-isomorphic2-isomorphism2-morphism===+=×???+?×ACActionactionalphabetantisymmetricAntisymmetryAoCAppendixArrarrowArrow Categoryarrow categoryassociativeassociative binary operationautofunctorAutomorphismautomorphismaxiom of choicebang frombang tobase categorybase functorbase pointbijectionBijectiveBinary Relationbinary relationbiterminatorCartesian ProductCartesian productcategorical definitionCategorical DefinitionsCategories of Structured SetsCategoryCategorycategorycategory actionCategory Examplescategory homomorphismCategory of CategoriesCategory of DigraphsCategory of Elements of a FunctorCategory of ForestsCategory of GroupsCategory of ListsCategory of MatricesCategory of MonoidsCategory of Natural NumbersCategory of PairsCategory of PosetsCategory of ProceduresCategory of ProsetsCategory of RelationsCategory of SetsCategory of StringsCategory of TosetsCategory of TreesCategory theoryCategory Theory in ProgrammingCayley’s representationCayley’s TheoremCayley’s Theoremcheckchoice functionClasscodcodcod+codomaincod×CollectionComma Categorycomma categorycommutativeCommutative Cubecommutative cubeCommutative Diagramcommutative diagramCommutative Squarecommutative squareCommutative Trianglecommutative trianglecommutecomponentcomposable paircomposecompositeCompositioncompositionComposition Functorcomposition functorcomposition rulesconcrete categoryconcretizablecongruence classCongruence Relationcongruence relationConstant Functorconstant functorConstructions on CategoriescontinuationContinuation-Passing Stylecontravariant functorContravariant Hom Functorcontravariant hom functorcosectioncoslice categorycoslice functorcosubobjectcosubstructurecovariant functorCovariant Hom Functorcovariant hom functorCPSctpDeterministic Finite Automatondeterministic finite automatonDFAdiagonal fill-indiagonal relationDiagramdiagramdigraphdigraph homomorphismdirect imageDirect Image Functordirect image functordirected edgedirected graphDiscrete Categorydiscrete categoryDisjoint Uniondisjoint uniondomdomdom+domaindom×dualedgeelementembeddingempty pathempty sequenceempty setendofunctorendofunctor categoryEndomorphismendomorphismepiepicepimorphismequalequality relationEquivalenceequivalenceequivalence classEquivalence of CategoriesEquivalence Relationequivalence relationequivalentessentially injectiveEssentially Injective Functoressentially surjectiveEssentially Surjective Functorexistential imageexistential image functorexponential categoryexponential setextensional setexternal homFAfactor throughfactorizationFactorization Systemfactorization systemFaithfulFamilyfillerfinal stateFinite Automatonfinite automatonforestforest homomorphismsForgetful Functorforgetful functorfree categoryFree Category Functorfree category functorfree diagramfree monoidFree Monoid Functorfree monoid functorFullfull subcategoryFully FaithfulfunctionFunctorFunctorfunctorfunctor categorygauntgaunt categorygeneralized elementglobal elementGlobal Element and Variable Elementglobal morphismglobal objectglobal pointgraphgraph homomorphismgroupgroup actiongroup homomorphismGroupoidgroupoidhom classhom functionHom Functorhom functorhom natural transformationHom Sethom sethomomorphismsHorizontal Categoryhorizontal categoryHorizontal Compositionhorizontal compositionhorizontal functori-celli-morphismIdempotentidempotentidentityidentity 1-cellidentity 2-cellidentity classidentity elementidentity morphismILimageinclusion functionInclusion Functorinclusion functorinitialinitial objectInitial Object and Terminal Objectinitial stateinjectionInjectiveInterchange Lawinterchange lawinternal hominverseinverse imageinverse image functorinvertibleisicisoisomorphicIsomorphismisomorphismisomorphism classIsomorphism of Categoriesisotoneisotone functionisotonicisotonic functionKleene closureKleene starlargelarge categorylayerleft actionleft cancellableleft inverseleft lifting propertyleft orthogonal classleft Quillen negationleft weak orthogonal classletterliftlifting propertyMapping Category to Programmingmembersmonicmonomonoidmonoid actionMonoid Actions as Functorsmonoid homomorphismmonoidal setmonoidoidmonomorphismMonomorphism and Epimorphismmonotonemonotone functionmonotonicmonotonic functionmorphismnatural isomorphismNatural TransformationNatural Transformationnatural transformationnaturalitynaturality conditionnaturally isomorphicnext statenext state functionNFAnodeNondeterministic Finite Automatonnondeterministic finite automatonnull objectobjectOFSone-object 2-categoryOne-Object Categoryone-object categoryone-object groupoidOOCOOGOpposite Categoryopposite categoryOpposite Functoropposite functoropposite natural transformationorder homomorphismordered listordered setorthogonalOrthogonal Factorization Systemorthogonal factorization systemover categoryparallelParallel Morphismpartial orderpartially ordered setpath categorypathsplanar forestpointed categoryPointed Objectpointed objectpointed setposetpowersetPowerset Functorpowerset functorpredicateprefactorization systempreimagePreimage Functorpreimage functorpreorderpreordered setpreservepresheafprocedureProduct Categoryproduct categoryproduct setprojection functionProjection Functorprojection functorproper cosubobjectproper quotient objectproper subobjectprosetpseudo-inversequotientQuotient Categoryquotient categoryquotient functorquotient objectquotient setquotient structurereflectreflexiveReflexivityRelationrelationReplete Subcategoryreplete subcategoryrepresentrepresentablerepresentable functorRepresentative Subcategoryrepresentative subcategoryretractretractionreturnright actionright cancellableright inverseright lifting propertyright orthogonal classright Quillen negationright weak orthogonal classrootrooted forestrooted treerun functionsectionsequencesetset theorysetoidshapesingleton setskeletalskeletal categoryskeletonSlislice categoryslice functorSli†smallsmall categorysourcesplit episplit epicsplit epimorphismsplit essentially surjectivesplit idempotentsplit monicsplit monosplit monomorphismSplit Morphismsrcsrcstart statestatestate diagramstate spacestate tablestiffstiff categoryStrict Monoidal Categorystrict monoidal categoryStrict Symmetric Monoidal Categorystrict symmetric monoidal categorystringString Diagramstring diagramsstripping functorStructure of 𝐂𝐚𝐭structured setSubcategorysubcategorysubmonoidsubobjectSubobject and Quotient ObjectsubsetsubstructureSum Categorysum categorysum setsurjectionSurjectivesymmetricSymmetrytagtagged pairtagged uniontargetTDFAtensor producttensor unitterminalterminal objecttgttgtThin Categorythin categorytopologytosettotaltotal orderTotalitytotally ordered settransitiontransition functiontransition relationtransitiveTransitivitytreetree homomorphismsTwo-Variable Hom Functortwo-variable hom functortyped actiontyped alphabetTyped Deterministic Finite Automatontyped deterministic finite automatontyped monoidtyped transition functionunder categoryunderlying digraphunderlying functorunderlying setunit objectUniversal Elementuniversal elementuniversal imageUniversal Image Functoruniversal image functoruniversal propertyvariable elementVertical Categoryvertical categoryVertical Compositionvertical compositionvertical functorverticesWeak Factorization Systemweak factorization systemweakly invertibleweakly orthogonalWFSwide subcategoryYoneda EmbeddingYoneda embeddingYoneda LemmaYoneda Lemmazero object{}{∗}××÷÷††ℕ→↓↠↣⇒∏∐∗∘∘∘+∘×∙∙∼∼≃≅⊆⊆⊗⊥⤖⧄⨾⨾𝐂𝐚𝐭𝐂𝐚𝐭b𝐂𝐚𝐭h𝐂𝐚𝐭v𝐃𝐠𝐫𝐅𝐬𝐭𝐆𝐫𝐩𝐋𝐢𝐬𝐭𝐌𝐚𝐭𝐫𝐌𝐨𝐧𝐍𝐚𝐭𝐎𝐨𝐜𝐎𝐨𝐠𝐏𝐚𝐢𝐫𝐏𝐨𝐬𝐏𝐫𝐨𝐜𝐏𝐫𝐨𝐬𝐑𝐞𝐥𝐒𝐞𝐭𝐒𝐞𝐭-Valued Functor𝐒𝐞𝐭-valued functor𝐒𝐞𝐭-Valued Functors as Typed Actions𝐒𝐞𝐭∗𝐒𝐭𝐫𝐓𝐨𝐬𝐓𝐫𝐞𝐞