Theorems · Theorem · category theory

CategoryTheory.IsAddModHom.addActionHom_apply

∀ {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) [inst_5 : CategoryTheory.IsAddModHom M f] (Z : C) (x : Z ⟶ X),
  (CategoryTheory.IsAddModHom.addActionHom f Z) x = CategoryTheory.CategoryStruct.comp x f

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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