Theorems · Theorem · category theory

CategoryTheory.Adjunction.shift_unit_app

∀ {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)
  (X : C),
  (CategoryTheory.shiftFunctor C a).map (adj.unit.app X) =
    CategoryTheory.CategoryStruct.comp (adj.unit.app ((CategoryTheory.shiftFunctor C a).obj X))
      (CategoryTheory.CategoryStruct.comp (G.map ((CategoryTheory.Functor.commShiftIso F a).hom.app X))
        ((CategoryTheory.Functor.commShiftIso G a).hom.app (F.obj X)))

Defined in

Mathlib.CategoryTheory.Shift.Adjunction

Cited by

1 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