Theorems · Theorem · category theory

CategoryTheory.IsAddModHom.map_vadd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {M : C}
  [inst_2 : CategoryTheory.AddMonObj M] {X : C} [inst_3 : CategoryTheory.AddModObj M X] {Y : C}
  [inst_4 : CategoryTheory.AddModObj M Y] (f : X ⟶ Y) [CategoryTheory.IsAddModHom M f] {Z : C} (m : Z ⟶ M) (x : Z ⟶ X),
  CategoryTheory.CategoryStruct.comp (m +ᵥ x) f = m +ᵥ CategoryTheory.CategoryStruct.comp x f

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.AddMonObjCategoryTheory.AddModObjCategoryTheory.AddModObjCategoryTheory.IsAddModHom