Theorems · Definition · category theory

CategoryTheory.ProdPreservesConnectedLimits.forgetCone

{C : Type u₂} →
  [inst : CategoryTheory.Category.{v₂, u₂} C] →
    [inst_1 : CategoryTheory.Limits.HasBinaryProducts C] →
      {J : Type v₂} →
        [inst_2 : CategoryTheory.SmallCategory J] →
          {X : C} →
            {K : CategoryTheory.Functor J C} →
              CategoryTheory.Limits.Cone (K.comp (CategoryTheory.Limits.prod.functor.obj X)) →
                CategoryTheory.Limits.Cone K

(Impl). Given a cone for (X × K -), produce a cone for K using the natural transformation γ₂

Defined in

Mathlib.CategoryTheory.Limits.Connected

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductsCategoryTheory.SmallCategory