Theorems · Definition · category theory

CategoryTheory.Limits.biproduct.lift

{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        {f : J → C} → [inst_2 : CategoryTheory.Limits.HasBiproduct f] → {P : C} → ((b : J) → P ⟶ f b) → (P ⟶ ⨁ f)

Given a collection of maps into the summands, we obtain a map into the biproduct.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Biproducts

Cited by

31 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBiproduct