Theorems · Theorem · category theory

CategoryTheory.Adjunction.commShiftIso_hom_app_counit_app_shift

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) (A : Type u_3) [inst_2 : AddMonoid A] [inst_3 : CategoryTheory.HasShift C A]
  [inst_4 : CategoryTheory.HasShift D A] [inst_5 : F.CommShift A] [inst_6 : G.CommShift A] [adj.CommShift A] (a : A)
  (Y : D),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso (G.comp F) a).hom.app Y)
      ((CategoryTheory.shiftFunctor D a).map (adj.counit.app Y)) =
    adj.counit.app ((CategoryTheory.shiftFunctor D a).obj Y)

Defined in

Mathlib.CategoryTheory.Shift.Adjunction

Cited by

2 results in Mathlib

Foundations

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

Assumes

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