Theorems · Theorem · category theory

CategoryTheory.ShiftedHom.comp_smul

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {M : Type u_4} [inst_1 : AddMonoid M]
  [inst_2 : CategoryTheory.HasShift C M] {X Y Z : C} {R : Type u_5} [inst_3 : Ring R]
  [inst_4 : CategoryTheory.Preadditive C] [inst_5 : CategoryTheory.Linear R C]
  [∀ (a : M), CategoryTheory.Functor.Linear R (CategoryTheory.shiftFunctor C a)] (r : R) {a b c : M}
  (α : CategoryTheory.ShiftedHom X Y a) (β : CategoryTheory.ShiftedHom Y Z b) (h : b + a = c),
  α.comp (r • β) h = r • α.comp β h

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHom

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftRingCategoryTheory.PreadditiveCategoryTheory.LinearCategoryTheory.Functor.Linear