Theorems · Definition · category theory

CategoryTheory.GradedObject.isColimitCofanMapObj

{I : Type u_1} →
  {J : Type u_2} →
    {C : Type u_4} →
      [inst : CategoryTheory.Category.{v_1, u_4} C] →
        (X : CategoryTheory.GradedObject I C) →
          (p : I → J) → [inst_1 : X.HasMap p] → (j : J) → CategoryTheory.Limits.IsColimit (X.cofanMapObj p j)

Given X : GradedObject I C, p : I → J and j : J, X.mapObj p j satisfies the universal property of the coproduct of those X i such that p i = j.

Defined in

Mathlib.CategoryTheory.GradedObject

Cited by

5 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GradedObject.HasMap