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OverfunctorFunctorPseudofunctorAnafunctorBifunctorUnderlying functorGroup functorAdjointCofunctorRepresentable functorFunctor categoryEndobifunctorOvercategoryContravariant functorFull functorMorphismMulticategoryContravarianceRelationEndofunctorFaithful functorPreradicalIdentity functorCocategoryProjectionBicategoryAdjunctAdjoint functorPresheafHyperfunctionKan extensionUnitParaproductCounitTricategoryUniversal propertyForgetful functorComma categoryGeneralized elementInverse systemMonoidal categorySupernumberYoneda functorCovectorCategory theoryComonadUltrafunctionScalar functionMonadTraciatorFormationHypersequentSemigroupoidMorphism setCategoryGraphSupermoduleProjectiveOverconeFunctionDirect sumOperatorProjectorGlobal elementMultifunctionDiagramCongruenceDirect productUniversal morphismOperator theoryVector functionAdjunctionAllegorySchoberSketchPoint functionMonomorphismProvectorCohomologySuperextensionApplicandFunctionalSurjective functionContramoduleCoendCartesian squarePluperfectionExponential objectHolomorphismCoaugmentationUltraproductSemigroup homomorphismDirect systemInitial objectGroup objectSuperoperatorProductK-functionCocharacterConstant morphism