Theorems · Definition · category theory

CategoryTheory.SingleFunctors.postcompIsoOfIso

{C : Type u_1} →
  {D : Type u_2} →
    {E : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
            {A : Type u_5} →
              [inst_3 : AddMonoid A] →
                [inst_4 : CategoryTheory.HasShift D A] →
                  [inst_5 : CategoryTheory.HasShift E A] →
                    (F : CategoryTheory.SingleFunctors C D A) →
                      {G G' : CategoryTheory.Functor D E} →
                        (e : G ≅ G') →
                          [inst_6 : G.CommShift A] →
                            [inst_7 : G'.CommShift A] →
                              [CategoryTheory.NatTrans.CommShift e.hom A] → F.postcomp G ≅ F.postcomp G'

The isomorphism F.postcomp G ≅ F.postcomp G' induced by an isomorphism e : G ≅ G' which commutes with the shift.

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

4 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShiftCategoryTheory.NatTrans.CommShift