Category constructors

Categories from scratch

Category constructors with nothing, a combinatorial, or an algebraic data structure as input:

category constructor	input	doctrine	package
`TerminalCategory`	nothing	almost all	CAP
`CatCat`	nothing	2-category	CAP
`FinSets`	nothing	elementary topos	FinSetsForCAP
`SkeletalFinSets`	nothing	elementary topos	FinSetsForCAP
`SkeletalFinGSets`	a (discrete) group	elementary topos	FinGSetsForCAP
`ProSetAsCategory`	a proset	thin	FreydCategoriesForCAP
`GroupAsCategory`	a (discrete) group	groupoid	FreydCategoriesForCAP
`RingAsCategory`	a unital ring	pre-additive	FreydCategoriesForCAP
`QuiverRows`	a quiver and a commutative ring k	k-linear	FreydCategoriesForCAP
`Algebroid`	a quiver and a commutative ring k	k-linear	Algebroids
`RepresentationCategory`	a group and a field	k-linear Abelian	GroupRepresentationsForCAP
`MatrixCategory`	a (skew)field k	k-linear Abelian	LinearAlgebraForCAP
`CategoryOfRows`	a unital ring	additive	FreydCategoriesForCAP
`CategoryOfColumns`	a unital ring	additive	FreydCategoriesForCAP
`LeftPresentations`	a computable ring	Abelian	ModulePresentationsForCAP
`RightPresentations`	a computable ring	Abelian	ModulePresentationsForCAP
`GradedLeftPresentations`	computable (multi) graded ring	Abelian	GradedModulePresentationsForCAP
`GradedRightPresentations`	computable (multi) graded ring	Abelian	GradedModulePresentationsForCAP
`CategoryOfHomalgFinitelyPresentedLeftModules`	a computable ring	Abelian	InternalModules
`CategoryOfHomalgFinitelyPresentedRightModules`	a computable ring	Abelian	InternalModules

Categories from categories

Category constructors which take one or several categories as input:

category constructor	input	package
`OppositeCategory`	a category	CAP
`ProductCategory`	several categories	CAP
`LinearClosure`	a commutative ring and a category	FreydCategoriesForCAP
`TwistedLinearClosure`	a commutative ring and a category	FreydCategoriesForCAP
`AdditiveClosure`	a pre-additive category	FreydCategoriesForCAP
`FreydCategory`	an additive category	FreydCategoriesForCAP
`CokernelImageClosure`	an additive category	FreydCategoriesForCAP
`CategoryOfAscendingFilteredObjects`	an Abelian category	ComplexesAndFilteredObjectsForCAP
`CategoryOfDescendingFilteredObjects`	an Abelian category	ComplexesAndFilteredObjectsForCAP
`RelCategory`	a category	FreydCategoriesForCAP
`GeneralizedMorphismCategoryByThreeArrows`	an Abelian category	GeneralizedMorphismsForCAP
`GeneralizedMorphismCategoryByCospans`	an Abelian category	GeneralizedMorphismsForCAP
`GeneralizedMorphismCategoryBySpans`	an Abelian category	GeneralizedMorphismsForCAP
`SerreQuotientsByCospans`	an Abelian category and a thick subcategory	GeneralizedMorphismsForCAP
`SerreQuotientsBySpans`	an Abelian category and a thick subcategory	GeneralizedMorphismsForCAP
`SerreQuotientsByThreeArrows`	an Abelian category and a thick subcategory	GeneralizedMorphismsForCAP
`AdelmanCategory`	an additive category	FreydCategoriesForCAP
`FunctorCategory` = `Hom`	a fin. dim. k-algebroid and k-linear Abelian category	FunctorCategories
`EnhancementWithAttributes`	an Abelian category	CategoriesWithAmbientObjects
`LeftActionsCategory`	an Abelian category	ActionsForCAP
`RightActionsCategory`	an Abelian category	ActionsForCAP
`LeftCoactionsCategory`	an Abelian category	ActionsForCAP
`RightCoactionsCategory`	an Abelian category	ActionsForCAP
`FullSubcategory`	a category	SubcategoriesForCAP
`Subcategory`	a category	SubcategoriesForCAP
`ChainComplexCategory`	an additive category	ComplexesCategories
`CochainComplexCategory`	an additive category	ComplexesCategories
`AsCategoryOfBicomplexes`	an additive category¹	Bicomplexes
`QuotientCategory`	a category and a two-sided ideal	QuotientCategories
`HomotopyCategory`	an additive category	HomotopyCategories
`DerivedCategory`	an Abelian category	DerivedCategories
`CategoryOfExactTriangles`	a triangulated category	TriangulatedCategories
`PositivelyZGradedCategory`	a category	GradedCategories
`CategoryOfLeftSModules`	a semi-simple tensor category²	InternalModules
`CategoryOfRightSModules`	a semi-simple tensor category²	InternalModules
`SliceCategory`	an object (of a category)	SubcategoriesForCAP
`SliceCategoryOverTensorUnit`	the tensor unit (of a monoidal category)	SubcategoriesForCAP
`PosetOfCategory`	a category	Locales
`ProsetOfCategory`	a category	Locales
`MeetSemilatticeOfDifferences`	a poset	Locales
`MeetSemilatticeOfMultipleDifferences`	a poset	Locales
`BooleanAlgebraOfConstructibleObjectsAsUnionOfDifferences`	a poset	Locales
`BooleanAlgebraOfConstructibleObjectsAsUnionOfMultipleDifferences`	a poset	Locales
`CategoryWithAmbientObject`	an Abelian category	CategoriesWithAmbientObjects
`IntrinsicCategory`	a category	IntrinsicCategories
`WrapperCategory`	a category	WrapperCategories
`LazyCategory`	a category	LazyCategories

¹ of complexes of complexes of an additive category ↩
² its positively graded closure ↩