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Theorems · Inductive type · category theory

CategoryTheory.OverClass

{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → C → Type v

OverClass X S is the typeclass containing the data of a structure morphism X ↘ S : X ⟶ S.

Defined in
Mathlib.CategoryTheory.Comma.Over.OverClass
Cited by
68 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
CategoryTheory.Category
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.over · cited by 76CategoryTheory.overAlgebraicGeometry.Scheme.Over · cited by 35Scheme.OverCategoryTheory.OverClass.asOver · cited by 16OverClass.asOverCategoryTheory.comp_over · cited by 14CategoryTheory.comp_overCategoryTheory.HomIsOver · cited by 11CategoryTheory.HomIsOverAlgebraicGeometry.Scheme.asOverProp · cited by 8Scheme.asOverPropCategoryTheory.OverClass.asOverHom · cited by 8OverClass.asOverHomAlgebraicGeometry.AffineSpace.hom_ext · cited by 8AffineSpace.hom_extAlgebraicGeometry.Scheme.Hom.asOverProp · cited by 7Hom.asOverPropAlgebraicGeometry.AffineSpace.map_over · cited by 5AffineSpace.map_overAlgebraicGeometry.Scheme.Cover.toPresieveOverProp · cited by 5Cover.toPresieveOverPropAlgebraicGeometry.AffineSpace.SpecIso_inv_over · cited by 4AffineSpace.SpecIso_inv_o…CategoryTheory.HomIsOver.comp_over · cited by 3HomIsOver.comp_overAlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp · cited by 3Cover.pullbackCoverOverPr…AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp' · cited by 3Cover.pullbackCoverOverPr…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.OverClassCITED BYCITES

Cites1

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Cited by99

Results whose statement or proof uses this declaration.