Theorems · Theorem · category theory

CategoryTheory.ModObj.lift_leftSMul_eq_lift_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {M : C}
  [inst_2 : CategoryTheory.MonObj M] {X : C} [inst_3 : CategoryTheory.ModObj M X] (Z : C) (x y : Z ⟶ X) (m : Z ⟶ M),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift m x)
        (CategoryTheory.ModObj.leftSMul M X) =
      CategoryTheory.CartesianMonoidalCategory.lift y x ↔
    m • x = y

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mod

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.ModObj