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Small categoryDiscrete categoryFunctor categorySieveCategoryObjectDiagramIdentity morphismDiagonal morphismTwist morphismConstant morphismGroup objectComma categoryFree categoryClassifying morphismUniversal morphismMonoidal categoryMorphismFunctorProjectionDirect productGroup schemeCategory theoryIdentity functorMulticategoryCoconeGlobal elementIsomorphismGeneralized elementSketchGraphCoslice categoryFibreMonomorphismBalanced categoryInitial objectHom-setGroup functorSplit monomorphismFull functorFormationMorphism setKernel pairCartesian closed categoryPresheafCokernelFaithful functorSchemoidCoconstant morphismBicartesian closed categorySitePushoutOverfunctorMonadTerminal objectTricategoryKernelBicategoryIntersectionAdjunctBimorphismSplit epimorphismNatural isomorphismNatural transformationConeRelationSectionZero morphismFiberSemigroupoidPullbackPrestackCategorical dualKleisli categoryCosectionAllegoryCocategoryGrothendieck topologyEquivalence of categoriesEpimorphismElementary toposInverseDirect systemIsogenyEqualizerZero objectInverse systemOvercategoryLimitAdjoint functorCartesian squareRepresentable functorComonadUnitAdjunctionToposColimitGroup actionGroupoidCoequalizer