Theorems · Theorem · category theory
CategoryTheory.comp_over
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) (S : C)
[inst_1 : CategoryTheory.OverClass X S] [inst_2 : CategoryTheory.OverClass Y S] [CategoryTheory.HomIsOver f S],
CategoryTheory.CategoryStruct.comp f (Y ↘ S) = X ↘ S- Cited by
- 14 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.overstatement · cited by 76
- CategoryTheory.OverClassstatement and proof · cited by 68
- CategoryTheory.HomIsOverstatement and proof · cited by 11
- CategoryTheory.HomIsOver.comp_overproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.OverClass.asOverHomproof · cited by 8
- CategoryTheory.comp_over_assocproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.isOver_iffproof · cited by 1
- AlgebraicGeometry.Scheme.PartialMap.isOver_iff_eq_restrictproof · cited by 1
- AlgebraicGeometry.ext_of_isDominant_of_isSeparated'proof · cited by 1
- AlgebraicGeometry.AffineSpace.reindex_compproof · cited by 1
- AlgebraicGeometry.Scheme.locallyCoverDense_of_leproof · cited by 1
- AlgebraicGeometry.AffineSpace.map_reindexproof · cited by 1
- AlgebraicGeometry.Scheme.RationalMap.isOver_iffproof · cited by 0