Theorems · Theorem · algebraic geometry

CategoryTheory.MorphismProperty.Over.mapComp.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] {X Y Z : T}
  [inst_2 : P.IsStableUnderComposition] {f : X ⟶ Y} (hf : P f) {g : Y ⟶ Z} (hg : P g) [inst_3 : Q.RespectsIso]
  (fg : X ⟶ Z) (hfg : fg = CategoryTheory.CategoryStruct.comp f g),
  CategoryTheory.MorphismProperty.Over.mapComp Q hf hg fg hfg =
    CategoryTheory.MorphismProperty.Over.mapComp Q hf hg fg hfg

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.RespectsIso