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FunctorOverfunctorIdentity functorUniversal morphismFull functorSmall categoryFaithful functorRepresentable functorGroup functorObjectYoneda functorIdentity morphismDiscrete categoryMonadSlice categoryDiagramMonomorphismContravariant functorFormationOvercategoryAdjoint functorDiagonal morphismEndofunctorPseudofunctorNatural transformationComma categoryMonoidal categoryDirect productProfunctorConstant morphismNatural isomorphismGlobal elementMorphismSieveClassifying morphismHom-setUnderlying functorGroup objectFree categoryUnitInitial objectAdjunctGeneralized elementContravarianceCategoryProjectionGraphAdjointIsomorphismCoconstant morphismMorphism setEpimorphismAdjunctionYoneda lemmaMulticategoryZero morphismEquivalence of categoriesCategorical dualBifunctorTerminal objectInverse systemBicartesian closed categoryYoneda embeddingUniversal propertyCartesian closed categoryPresheafCofunctorCartesian natural transformationZero objectDirect systemInverseSketchFiberFibreTwist morphismCokernelAdditive groupEndobifunctorCoconeLeft inverseGroup schemeElementary toposKleisli categoryBimorphismRelationSplit monomorphismNatural numbers objectPrestackExponential objectGrothendieck topologyCocategoryForgetful functorRight inverseKan extensionCategory theoryCocompletionEqualizerNull objectCounitSplit epimorphism