Theorems · Theorem · algebraic geometry

CategoryTheory.MorphismProperty.Over.mapId.congr_simp

∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] {P : CategoryTheory.MorphismProperty T}
  (Q : CategoryTheory.MorphismProperty T) [inst_1 : Q.IsMultiplicative] [inst_2 : P.IsStableUnderComposition]
  [inst_3 : P.IsMultiplicative] [inst_4 : Q.RespectsIso] (X : T) (f : X ⟶ X)
  (hf : f = CategoryTheory.CategoryStruct.id X),
  CategoryTheory.MorphismProperty.Over.mapId Q X f hf = CategoryTheory.MorphismProperty.Over.mapId Q X f hf

Defined in

Mathlib.AlgebraicGeometry.ColimitsOver

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIso