Theorems · Theorem · category theory

CategoryTheory.IsPushout.of_map_of_faithful

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) {W X Y Z : C} {f : W ⟶ X} {g : W ⟶ Y} {h : X ⟶ Z} {i : Y ⟶ Z}
  [CategoryTheory.Limits.ReflectsColimit (CategoryTheory.Limits.span f g) F] [F.Faithful],
  CategoryTheory.IsPushout (F.map f) (F.map g) (F.map h) (F.map i) → CategoryTheory.IsPushout f g h i

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimitCategoryTheory.Functor.Faithful