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Functor categoryIdentity morphismConstant morphismDiagonal morphismUniversal propertyGlobal elementMonomorphismFunctorZero morphismObjectMorphismMonadIdentity functorClassifying morphismCoconstant morphismOverfunctorZero objectFull functorSmall categoryIsomorphismTerminal objectDirect productInitial objectProjectionTwist morphismNull objectNatural transformationMonoidal categoryGroup objectDiscrete categoryFaithful functorDiagramMorphism setEpimorphismAdjunctBimorphismGeneralized elementFree categoryNatural isomorphismComma categorySlice categorySplit monomorphismFormationContravariant functorHom-setInverseMulticategoryUnitSieveCategoryGroup functorCokernelRepresentable functorYoneda functorAdjunctionAdjoint functorEquivalence of categoriesDirect systemMonodromyContravariancePseudofunctorNatural numbers objectGraphOvercategoryCartesian closed categoryInverse systemEndofunctorCategorical dualFibreYoneda lemmaPushoutLeft inverseSplit epimorphismKernelComonadCoconeProfunctorUnderlying functorKernel pairRight inverseExponential objectAdjointAutomorphismBicartesian closed categoryFiberComorphismOverconeContactomorphismColimitBalanced categoryKleisli categoryDirect limitAutomorphism groupSemigroupoidIntersectionElementary toposCocompletionEqualizerCartesian natural transformationPullback