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Small categorySubcategoryFunctor categoryIdentity functorRepresentable functorInitial and terminal objectsCategory of topological spacesFunctorCategory of setsDiagonal morphismIdentity morphismClosed monoidal categoryFull functorConcrete categoryNerveInverse systemHom functorCategoryNatural transformationDirect systemMonoidSieveModel categoryHom-setSubfunctorMorphismDiscrete categoryGrothendieck topologyProduct categoryFormationCartesian closed categoryCategory of modulesEquivalence of categoriesClosed categoryAbelian categoryMonoidal functorSlice categorySubobjectQuotient categoryCatamorphismEnriched categoryCategorificationFaithful functorF-coalgebraMonoidal categoryCategory of relationsYoneda functorElementYoneda embeddingMonadMonomorphismDerived categorySubobject classifierCoproductCohomologyAdjoint functorsTriangulated categoryBiproductImageContravariant functorFukaya categoryProductConstructible universeCosmosObjectCategory theoryElementary toposUnitSymplectomorphismGroup schemeCoequalizerAutomorphism groupToposSymmetric groupZero morphismAdditive categoryFree categoryIsometry groupInclusion functionAffine groupCanonical mapSymmetric monoidal categoryMulticategoryCosetCotangent bundleFull and faithful functorsIsogenyOutline of category theoryGeneratorEpimorphismCommutator subgroupDagger categorySimple homotopy theoryCompact groupAdjoint functorFamily of setsNatural isomorphismAllegoryAbstract simplicial complexHomological algebra