Theorems · Theorem · category theory

CategoryTheory.MonObj.comp_mul_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {M X Y : C} [inst_2 : CategoryTheory.MonObj M] (f : X ⟶ Y) (g₁ g₂ : Y ⟶ M) {Z : C} (h : M ⟶ Z),
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (g₁ * g₂) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp f g₁ * CategoryTheory.CategoryStruct.comp f g₂) h

Defined in: Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by: 0 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.MonObj

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.MonObjstatement and proof · cited by 199
CategoryTheory.Hom.monoidstatement · cited by 52
CategoryTheory.MonObj.comp_mulproof · cited by 10

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