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FunctorMonoidal categoryRepresentable functorMorphismMonoidModule homomorphismClosed monoidal categoryFull and faithful functorsKleisli categoryMonadMonomorphismEnriched categoryNatural transformationClosed categoryQuotient categoryHom functorApplicative functorSymplectomorphismFunctor categoryF-algebraString diagramImageExact functorConeProjective objectRing homomorphismF-coalgebraBundle mapTriangulated categoryTor functorEquivalence of categoriesAlgebra homomorphismInitial and terminal objectsHomomorphismCosmosCategory of relationsMonad transformerMonotone class theoremConcrete categoryProfunctorCategory of small categoriesAbelian categorySubcategorySectionGraph homomorphismMonotonic functionCategory of setsCellular homologyDerived functorCategory of topological spacesExt functorAdjoint functorsSemigroupAdditive categoryCoequalizerProjectionDiagramHomotopy groupCompletion of a ringGrothendieck topologyCartesian closed categoryElementDualSpanSymmetric monoidal categoryUniversal propertyHomotopy theoryBiproductMorita equivalenceSimplicial homologyAlgebra representationModel categoryIsomorphismCanonical mapMotivic cohomologyProduct categoryMultilinear formPreadditive categoryGroup actionEndomorphismHomological algebraMetrizable spaceExponential objectFundamental groupoidHigher-dimensional algebraStructureMorphism of algebraic varietiesCategory of modulesFlat moduleDerived categorySpectral spaceSimple homotopy theoryDiffeomorphismPushforwardCommutative ringCompact-open topologyMapping class groupProper morphismAllegoryFunctional calculus