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OverfunctorUnderlying functorFunctor categoryFull functorRepresentable functorOverconeContravarianceEndofunctorProfunctorFunctorFaithful functorComma categoryAdjointIdentity functorContravariant functorMulticategoryYoneda functorGroup functorPseudofunctorCocategoryFormationBifunctorMonadBicategorySmall categoryPrestackUniversal morphismDirect productKan extensionPregroupoidMonoidal categoryTricategoryElementary toposDiagramAdjunctInitial objectProjectionUnitYoneda embeddingAdditive groupCoslice categoryGlobal elementAdjoint functorSiteMonomorphismToposComonadBalanced categoryDiscrete categoryNatural isomorphismGeneralized elementPresheafAbstract nonsenseCofunctorCategory theoryEndobifunctorRelationHom-setConstant morphismYoneda lemmaMorphism setCartesian closed categoryAllegoryBicartesian closed categoryColimitCategorical dualInverse limitCategoryAnafunctorInverse systemAdjunctionEquivalence of categoriesObjectForgetful functorConeGroup objectLimitCoconstant morphismEpimorphismExponential objectFree categoryTerminal objectCoconeInverseIntersectionMorphismSectionSketchCocompletionKleisli categorySchoberBilimitGoguen categorySlice categoryGrothendieck topologyZero objectDirect limitPushoutGeneric elementZero morphism