Theorems · Definition · category theory

CategoryTheory.Comma.opFunctorCompFst

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {T : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} T] →
            (L : CategoryTheory.Functor A T) →
              (R : CategoryTheory.Functor B T) →
                (CategoryTheory.Comma.opFunctor L R).leftOp.comp (CategoryTheory.Comma.fst R.op L.op) ≅
                  (CategoryTheory.Comma.snd L R).op

Composing the leftOp of opFunctor L R with fst L.op R.op is naturally isomorphic to snd L R.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

3 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category