Category:Category theory
branch of mathematics studying categories, functors, and natural transformations | |||||
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English: Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them.
Category:Subdivisions of mathematics
Category:Mathematics by topic
Category:Mathematical structures
Category:Functions and mappings
Category:Foundations of mathematics
Category:Fields of abstract algebraPages in category "Category:Category theory"
- Template:2-category interchange law
- Category:Morphisms
- Category:Comma categories
- Category:Commutative diagrams
- Category:Free algebraic structures
- Category:Functors
- Category:Higher category theory
- Category:Module theory
- Category:Monoidal category
- Category:Operads
- Category:Quivers (graph theory)
- File:2 point discrete space.png
- File:AlgebraicGroup diagrams.gif
- File:Amalcatresugwe.tif
- File:Amalgcatlimfqwfq.tif
- File:Amalwejhcatlimfqwfq.tif
- File:Anafunctor (span).pdf
- File:Anafunctor (span).svg
- File:Applicative Form of Monoidal Coherence Map 01.svg
- File:Arrow diagram transitive.png
- File:Associativity Coherence of Tensorial Strengths.svg
- File:Baby Category 1 plus 1.svg
- File:Baby Category 1.svg
- File:Baby Category 2.svg
- File:BabyCategory 1.png
- File:BabyCategory 1plus1.png
- File:BabyCategory 2.png
- File:Bialgebra4a.svg
- File:Braid category hexagon.svg
- File:Braid category inverse hexagon.svg
- File:Carré cartésien diagramme.png
- File:Carré cartésien.png
- File:Category SVG.svg
- File:Coker-simple.svg
- File:Coker-simple2.svg
- File:Cokernel-thm1.svg
- File:Cokernel-thm2-1.svg
- File:Cokernel-thm2-2.svg
- File:Commutative Diagram 2.jpg
- File:Composition of morphisms1.jpg
- File:Composition of Roofs in Derived Category.pdf
- File:Compositionoffunctions.png
- File:Connection between comma category and universal properties.svg
- File:Connection between universal diagrams and comma categories.svg
- File:Dagger compact category (diagram).png
- File:Dagger compact category (diagram).svg
- File:Dagger Compact Category.svg
- File:Definition-of-a-nodal-decomposition.jpg
- File:Delta maps.svg
- File:DeltaFunctorLongExactSequence.png
- File:Determinant as a natural transformation.svg
- File:Diag ax cat.gif
- File:Diagram of geometric categories.png
- File:Diagram of geometric categories.svg
- File:Diagram przemienny.png
- File:Diagramgalileioper.png
- File:Discrete category.svg
- File:Distributive law monads mult1.svg
- File:Distributive law monads mult2.svg
- File:Distributive law monads unit1.svg
- File:Distributive law monads unit2.svg
- File:Eckman hilton clock.svg
- File:Eckmanhilton.jpg
- File:Enrichedidentity.png
- File:Enrichedmult.png
- File:Enrichment-2.jpg
- File:Epimorphism scenarios.svg
- File:Exact couple.png
- File:Extension-3.jpg
- File:F Algebra Associativity Commutative Diagram.svg
- File:F Algebra Identity Commutative Diagram.svg
- File:F Algebra Inverse Commutative Diagram.svg
- File:Factorisation.svg
- File:Factorization system functoriality.png
- File:Factorization system orthogonality.png
- File:Fibered product detail.svg
- File:Fibre bundle local trivial.svg
- File:Free-category-ump.svg
- File:Free-object-universal-property.svg
- File:Fullness of a diagonal functor.svg
- File:FunctionDecompCD.jpg
- File:Functor Strength By Tensorial Strength.svg
- File:Functor.png
- File:Functoriality (2).svg
- File:Functoriality long exact sequence.svg
- File:Functors Between Objects and Morphisms of C.pdf
- File:Fundamental Homomorphism Theorem v2.svg
- File:Funtori paralleli kf.png
- File:Galileiiidiagram.png
- File:Globular set.svg
- File:Graphical illustration of Hom functor (covariant).svg
- File:GrothendieckGroupAsFunctor.PNG
- File:Group associative categories.svg
- File:Group operation image.tif
- File:Hochhebungseigenschaft.png
- File:Hom functor.svg
- File:Homotopy lifting property.png
- File:Horizontal composition of natural transformations.svg
- File:Hurewicz2 (corrected).svg
- File:Hypermorphisms.pdf
- File:Initial and terminal object.png
- File:InitialAndFinalObjectsInTheCategoryOfAdjunctions.png
- File:Isomorphisme d'une catégorie1.png
- File:Jean Bénabou en 2019.jpg
- File:Joyal lifting theorem 2.svg
- File:Joyal lifting theorem.svg
- File:Kategoria przecinkowa.png
- File:Kategória1.png
- File:Ker-simple.svg
- File:Ker-simple2.svg
- File:Kernel of morphism.svg
- File:Kernel-thm1.svg
- File:Kernel-thm2-1.svg
- File:Kernel-thm2-2.svg
- File:Kernel.svg
- File:Kleisli Category - morphism composition.png
- File:Kleisli Category - morphism composition.svg
- File:Kompositiongundf.png
- File:Lax monoidal funct assoc.png
- File:Left Unit Coherence of Tensorial Strengths.svg
- File:LiftingProperties.png
- File:List object definition.svg
- File:Luonnollinen muunnos.png
- File:Luonnollisen muunnoksen ehto.png
- File:Luonnollisen muunnoksen komponentit.png
- File:Luonnollisen muunnoksen ylinuolet.png
- File:Mappings-as-moduli.png
- File:Minoid.png
- File:Model category lifting.png
- File:Model category retract.png
- File:Modification in category theory.png
- File:MonadDistrEtaPString.svg
- File:MonadDistrMuPString.svg
- File:Monoid multiplication.svg
- File:Monoid unit svg.svg
- File:Monoidal category pentagon.svg
- File:Monoidal category triangle.svg
- File:Monoidal Coherence Map from Applicative Formulation.svg
- File:Monoidal natural transformation multiplication.svg
- File:Monoidal natural transformation unit.svg
- File:Monoidal2.svg
- File:Monomorphism pullback square.png
- File:Monomorphism scenarios.svg
- File:Morphism-Composition.svg
- File:Morphism.svg
- File:MorphismInTheCategoryOfAdjunctions.png
- File:Natural Transformation between two functors.svg
- File:Natural transformation diagram.svg
- File:Natural transformation.svg
- File:Nodal-and-basic-decomposition-1.jpg
- File:Nodal-decomposition-notations.jpg
- File:OperadTreeCompose2.svg
- File:OperadTreeCompose3.svg
- File:OperadTreeCompose5.svg
- File:OperadTreeCompose6.svg
- File:Opposite group nature.svg
- File:Pentagonal diagram for monoidal categories.svg
- File:Podkategoria reflektywna.png
- File:Podnoszenie homotopii.png
- File:Polygraph (mathematics).svg
- File:Prod chain.svg
- File:Projective object.svg
- File:PullbackS.PNG
- File:Pure Operator By Tensorial Strength.svg
- File:Pystyliitos.png
- File:Quasifibration-fibration.png
- File:Quasifibration-via-hofibre.svg
- File:Quiver Morphism Start Diagram.svg
- File:Quiver Morphism Target Diagram.svg
- File:Refinement.jpg
- File:Relations category op.svg
- File:Relations category.svg
- File:RetractOfMorphism.png
- File:Right Kan extension universal property diagram.PNG
- File:Right Kan Extension.png
- File:Sample Bratteli diagram.svg
- File:Section (théorie des catégories).png
- File:Simple category.svg
- File:Slice category.png
- File:Smart Plant.jpg
- File:Stone functor.svg
- File:String diagram adjunction.svg
- File:String diagram counit.svg
- File:String diagram identity.svg
- File:String diagram unit.svg
- File:Strong monad associative.svg
- File:Strong monad commutation.png
- File:Strong monad commutation.svg
- File:Strong monad left unit.svg
- File:Strong monad multiplication.svg
- File:Strong monad unit.svg
- File:SubobjectClassifier-03.png
- File:Symmetric monoidal associativity coherence.png
- File:Symmetric monoidal category swap.svg
- File:Symmetric monoidal inverse law.png
- File:Tensorial Costrength By Tensorial Strength.svg
- File:Tensorial Strength By Functor Strength.svg
- File:Tensorial Strength By Pure Operator.svg
- File:TermAlgebra-Diagram-01.svg
- File:Terminal and initial object.svg
- File:Topcatejigre.tif
- File:Trace diagram associativity.svg
- File:Trace diagram dinaturality.svg
- File:Trace diagram naturality 1.svg
- File:Trace diagram naturality 2.svg
- File:Trace diagram superposition.svg
- File:Trace diagram vanishing.svg
- File:Trace diagram yanking.svg
- File:Transitive-closure-cs.svg
- File:Transitive-closure.svg
- File:Trasfnat composizione orizzontale elem kf.png
- File:Trasfnat composizione orizzontale kf.png
- File:Trasfnat composizione verticale kf.png
- File:Trasformazione naturale kf.png
- File:Uinit-counit-1.png
- File:Uniqueness-of-nodal-decomposition-2.jpg
- File:Unit coherence isomorphisms.svg
- File:Unit-counit.png
- File:Universal morphisms appear as the unit and counit of adjunctions.svg
- File:Universal-property-products.svg
- File:Vertical composition of natural transformations.svg
- File:Waldhausen cat.png