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Equivalence of categoriesExact functorExact sequenceEquivalence classSplit exact sequenceIsomorphism theoremsSubcategoryAbelian categoryConjugacy classAlgebra homomorphismDistributive propertyRepresentation theoremCohomologyGroup homomorphismQuotient categorySplitting fieldFundamental groupHomomorphismCoequalizerHurewicz theoremClosed monoidal categoryCartesian closed categorySimple homotopy theoryTelescoping seriesInitial and terminal objectsMorphismCommutative diagramDerived categorySchur product theoremEquivalence relationAffine groupCayley's theoremCongruence relationGroup isomorphismMatrix splittingBounded inverse theoremSimplicial homologyFive lemmaSperner's lemmaEquationLefschetz fixed-point theoremCategory of small categoriesRegular sequenceAdjoint functorsSpectral sequenceEquivalenceSemisimple lie algebraCategory of modulesInjective functionIsogenyLie's third theoremCommutator subgroupHomogeneous relationIncidence algebraAbelian groupAbel's theoremExponential sheaf sequenceSymmetric groupGrothendieck groupInclusion mapPerfect groupEquivariant cohomologyRecurrence relationLinear algebraic groupChain complexOrdered exponentialNatural transformationSolvable groupHermitian adjointAliquot sequenceOrthogonal polynomialsTransitive relationLefschetz hyperplane theoremTranspose of a linear mapAxiom of choiceHilbert's basis theoremSymmetric polynomialHom functorEquivariant mapIsometryModel categoryIdentityTriangle inequalityGenerating set of a groupExcision theoremLimitPoisson algebraLinear relationDual spaceSymmetric graphFinitely generated abelian groupMonoidal functorClosed-subgroup theoremGroup actionLogical equivalenceCongruence subgroupHomographyCompactness theoremSymmetric algebraTransitive closure