Theorems · Theorem · category theory

CategoryTheory.SmallObject.functorObj_comm_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {I : Type w} {A B : I → C} (f : (i : I) → A i ⟶ B i) {S X : C}
  (πX : X ⟶ S)
  [inst_1 :
    CategoryTheory.Limits.HasColimitsOfShape (CategoryTheory.Discrete (CategoryTheory.SmallObject.FunctorObjIndex f πX))
      C]
  [inst_2 :
    CategoryTheory.Limits.HasPushout (CategoryTheory.SmallObject.functorObjTop f πX)
      (CategoryTheory.SmallObject.functorObjLeft f πX)]
  {Z : C} (h : CategoryTheory.SmallObject.functorObj f πX ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.SmallObject.functorObjTop f πX)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SmallObject.ιFunctorObj f πX) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.SmallObject.functorObjLeft f πX)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.SmallObject.ρFunctorObj f πX) h)

Defined in

Mathlib.CategoryTheory.SmallObject.Construction

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasPushout