Theorems · Theorem · category theory

CategoryTheory.Subobject.eq_of_comp_arrow_eq

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {P : CategoryTheory.Subobject Y}
  {f g : X ⟶ CategoryTheory.Subobject.underlying.obj P},
  CategoryTheory.CategoryStruct.comp f P.arrow = CategoryTheory.CategoryStruct.comp g P.arrow → f = g

Two morphisms into a subobject are equal exactly if the morphisms into the ambient object are equal

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

31 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category