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MorphismNatural transformationNatural isomorphismFunctor categorySymplectomorphismIsometryGeometric transformationDiagonal morphismUniversal propertyIsogenyCanonical formHomographyCartesian closed categoryIsomorphismHomotopy theoryMappingIdentity morphismIdentity functorLocal diffeomorphismMonoidImageInitial and terminal objectsProjectionOpen and closed mapsAlgebra homomorphismTopological propertyEquivalence of categoriesProduct topologyRepresentable functorInclusion mapIsometry groupGraph homomorphismRepresentation theoremCategory of topological spacesHomeomorphismHomomorphismEuclidean topologyCotangent complexConnectorBundle mapCantor spaceMonomorphismGraph automorphismMetrizable spaceQuotient categoryLinear mapAutomorphismFunctorModule homomorphismGroup isomorphismLocal homeomorphismGroup actionConformal mappingEdge-transitive graphEndomorphismSubcategoryTranspose of a linear mapCategorificationHolomorphic vector bundleGeometric topologyFull functorCompact-open topologyConstant morphismAffine groupContinuous linear operatorOperatorInjective functionHurewicz theoremExponential objectGroup ringProjectivizationMeasurable functionExact sequenceInclusion functionField normSubmanifoldCanonical transformationCategory theoryMonotonic functionSurjective functionSimple homotopy theoryConstructive proofMusical isomorphismAbelian categoryClosed monoidal categoryCovering groupCounitIsomorphism theoremsEquivariant mapFormationArithmetic groupNumber-theoretic functionConcrete categoryGeneral topologyMapping class groupBilinear mapExponential mapRelative homologySieveRigid transformation