Theorems · Theorem · category theory

CategoryTheory.ShiftedHom.map_smul

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [inst_2 : AddMonoid M]
  [inst_3 : CategoryTheory.HasShift C M] [inst_4 : CategoryTheory.HasShift D M] {X Y : C} {R : Type u_5}
  [inst_5 : Ring R] [inst_6 : CategoryTheory.Preadditive C] [inst_7 : CategoryTheory.Linear R C]
  [inst_8 : CategoryTheory.Preadditive D] [inst_9 : CategoryTheory.Linear R D] (r : R) {a : M}
  (α : CategoryTheory.ShiftedHom X Y a) (F : CategoryTheory.Functor C D) [inst_10 : F.CommShift M]
  [CategoryTheory.Functor.Linear R F], (r • α).map F = r • α.map F

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHom

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftRingCategoryTheory.PreadditiveCategoryTheory.LinearCategoryTheory.PreadditiveCategoryTheory.LinearCategoryTheory.Functor.CommShiftCategoryTheory.Functor.Linear