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Natural isomorphismCartesian natural transformationUnitAdjunctionAdjoint functorFunctor categoryConstant morphismFunctorUniversal morphismFormationIdentity morphismMorphismDiagonal morphismMonomorphismEquivalence of categoriesNatural numbers objectProjectionTwist morphismCounitYoneda lemmaDirect productContravariant functorOverfunctorCoconstant morphismIsomorphismObjectIdentity functorFull functorDiagramMonoidal categoryAdjunctClassifying morphismContravarianceUniversal propertyGlobal elementInverse systemEpimorphismCoaugmentationSlice categoryPullbackZero morphismGraphMorphism setPushoutKernel pairCategoryDirect systemHom-setPseudofunctorCategorical dualInitial objectFaithful functorInverseGroup objectSplit monomorphismYoneda functorGeneralized elementEqualizerCoequalizerBimorphismTerminal objectFree categoryRepresentable functorMulticategoryCokernelComma categoryCoconeIntersectionExponential objectProfunctorBicartesian closed categorySmall categoryAdjointMonodromyContactomorphismUnderlying functorLeft inverseAutotransformationRight inverseDiscrete categoryEndofunctorSplit epimorphismSievePresheafOvercategoryRelationComorphismFiberAutoequivalenceConeBifunctorAbstract nonsenseSketchHomomorphismFibreKernelZero objectWitt groupCofunctorOrthomorphism