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Functor categoryFunctorOvercategoryFull functorOverconeProfunctorContravariant functorEndofunctorUnderlying functorIdentity functorFaithful functorPseudofunctorUniversal morphismBifunctorRepresentable functorMonomorphismConstant morphismContravarianceProjectionGlobal elementAdjunctCoconstant morphismGroup functorInverseYoneda functorEndobifunctorEpimorphismMorphismCofunctorMonadMorphism setDiagramClassifying morphismPresheafSplit epimorphismZero morphismSmall categoryDiagonal morphismHom-setBimorphismAdjointSplit monomorphismGeneralized elementDiscrete categoryFormationIsomorphismObjectIdentity morphismFiberNatural isomorphismPushoutFibreMulticategoryDirect productGraphNatural transformationPregroupoidPrestackComma categoryLeft inverseYoneda embeddingAdjoint functorGroup objectCokernelMonoidal categoryRight inverseTwist morphismInverse systemUnitForgetful functorAnafunctorSieveAdjunctionInitial objectFree categoryToposKernel pairSlice categoryEqualizerEquivalence of categoriesYoneda lemmaAdditive groupTricategoryComonadPullbackCartesian natural transformationCategorical dualKan extensionKernelContactomorphismUniversal propertyCocategoryIsogenyIntersectionElementary toposCocompletionRegular mapColimitBalanced categoryMonodromy