Theorems · Theorem · category theory

CategoryTheory.Limits.limit_obj_ext_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type u₁} [inst_1 : CategoryTheory.Category.{v₁, u₁} J]
  {K : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} K]
  {H : CategoryTheory.Functor J (CategoryTheory.Functor K C)} [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C]
  {k : K} {W : C} {f g : W ⟶ (CategoryTheory.Limits.limit H).obj k},
  f = g ↔
    ∀ (j : J),
      CategoryTheory.CategoryStruct.comp f ((CategoryTheory.Limits.limit.π H j).app k) =
        CategoryTheory.CategoryStruct.comp g ((CategoryTheory.Limits.limit.π H j).app k)

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Basic

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShape