Theorems · Theorem · category theory

CategoryTheory.Subobject.mk_lt_mk_iff_of_comm

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X A₁ A₂ : C} {i₁ : A₁ ⟶ X} {i₂ : A₂ ⟶ X}
  [inst_1 : CategoryTheory.Mono i₁] [inst_2 : CategoryTheory.Mono i₂] (f : A₁ ⟶ A₂),
  CategoryTheory.CategoryStruct.comp f i₂ = i₁ →
    (CategoryTheory.Subobject.mk i₁ < CategoryTheory.Subobject.mk i₂ ↔ ¬CategoryTheory.IsIso f)

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

0 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoCategoryTheory.Mono