Theorems · Definition · category theory

CategoryTheory.Subobject.lowerCompRepresentativeIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      (F : CategoryTheory.Functor (CategoryTheory.MonoOver Y) (CategoryTheory.MonoOver X)) →
        (CategoryTheory.Subobject.lower F).comp CategoryTheory.Subobject.representative ≅
          CategoryTheory.Subobject.representative.comp F

Applying lower F and then representative is isomorphic to first applying representative and then applying F.

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category