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AdjointAdjunctUnitAdjunctionCounitEquivalence of categoriesFunctor categoryFunctorNatural transformationComma categoryConstant morphismPseudofunctorFull functorIdentity functorRepresentable functorCategorical dualDiagramContravariant functorFaithful functorNatural isomorphismCoequalizerComonadCoconstant morphismGroup functorBiadjunctionProfunctorYoneda functorCocategoryInverse systemDiagonal morphismCofunctorContravarianceMonomorphismUniversal morphismOverfunctorIsomorphismMonoidal categoryInverseUnderlying functorIdentity morphismFormationDirect systemCartesian natural transformationEndofunctorMonadYoneda lemmaCoconeCoaugmentationEqualizerOvercategoryBifunctorCoendObjectTwist morphismPushoutCocompletionGroup objectDiscrete categoryLeft inverseCategoryAdditive groupComatrixAssociateBicartesian closed categoryProjectionEndobifunctorKernel pairMorphismBijectionPreradicalColimitZero morphismCohomologyDirect productInitial objectIntersectionRight inverseSplit monomorphismDirect limitConeTraciatorSurjectionEpimorphismGraphKleisli categoryYoneda embeddingAutoequivalenceUniversal propertySlice categoryGroupoidKan extensionAdjugatePullbackQuotient mapInverse limitCotranslationTerminal objectMorphism setZero objectCokernel