Theorems · Theorem · category theory

CategoryTheory.HomIsOver.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} [self : CategoryTheory.HomIsOver f S],
  CategoryTheory.CategoryStruct.comp f (Y ↘ S) = X ↘ S

Defined in: Mathlib.CategoryTheory.Comma.Over.OverClass
Cited by: 3 results in Mathlib
Foundations: Depth 10 from the axioms · uses no axioms
Assumes: CategoryTheory.HomIsOver

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Cites6

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

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.comp_overproof · cited by 14
AlgebraicGeometry.Scheme.Hom.isOver_iffproof · cited by 0
AlgebraicGeometry.Scheme.PartialMap.isOver_toRationalMap_iff_of_isSeparatedproof · cited by 0