Theorems · Theorem · category theory

CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ A₂ : C} {f₁ : A₁ ⟶ B} {f₂ : A₂ ⟶ B}
  [inst_1 : CategoryTheory.Mono f₁] [inst_2 : CategoryTheory.Mono f₂] (g : A₁ ⟶ A₂)
  (w : CategoryTheory.CategoryStruct.comp g f₂ = f₁),
  (CategoryTheory.Subobject.mk f₁).ofLE (CategoryTheory.Subobject.mk f₂) ⋯ =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.underlyingIso f₁).hom
      (CategoryTheory.CategoryStruct.comp g (CategoryTheory.Subobject.underlyingIso f₂).inv)

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoCategoryTheory.Mono