Theorems · Theorem · category theory

CategoryTheory.Adjunction.LeftAdjointCommShift.compatibilityUnit_iso

∀ {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 : AddGroup A] [inst_3 : CategoryTheory.HasShift C A]
  [inst_4 : CategoryTheory.HasShift D A] [inst_5 : G.CommShift A] (a : A),
  CategoryTheory.Adjunction.CommShift.CompatibilityUnit adj (CategoryTheory.Adjunction.LeftAdjointCommShift.iso adj a)
    (CategoryTheory.Functor.commShiftIso G a)

The commutation isomorphisms of Adjunction.LeftAdjointCommShift.iso are compatible with the unit of the adjunction.

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.CategoryAddGroupCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShift