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Full functorFunctorIdentity functorRepresentable functorFunctor categoryOverfunctorContravariant functorPseudofunctorMonomorphismYoneda functorDiscrete categoryConstant morphismHom-setUniversal morphismMorphism setIdentity morphismEndofunctorMorphismSmall categoryIsomorphismOvercategoryPresheafDiagonal morphismInverseUnderlying functorGroup functorProfunctorAdjoint functorNatural isomorphismGraphDiagramAdjunctContravarianceYoneda lemmaProjectionClassifying morphismAdjointCoconstant morphismEpimorphismMonoidal categoryInverse systemMonadDirect productBifunctorSplit monomorphismFormationSieveSplit epimorphismGlobal elementZero morphismFibreFiberGeneralized elementGroup objectEquivalence of categoriesLeft inverseBijectionAdjunctionUniversal propertyHomomorphismEqualizerRight inverseUnitTwist morphismFibrationSlice categoryBimorphismObjectYoneda embeddingIsogenyEndobifunctorForgetful functorDirect systemComma categoryFree categoryCofunctorProfinite groupBalanced categorySurjectionNatural transformationMulticategoryInitial objectLimitKleisli categorySemigroup homomorphismTraciatorInjectivityRegular mapKernelGrothendieck topologyRing homomorphismQuotient mapInverse limitCategorical dualPrestackDirect limitCategoryAllegoryCocompletionOvercone