Theorems · Theorem · category theory

CategoryTheory.FinitaryPreExtensive.hasPullbacks_of_is_coproduct

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.FinitaryPreExtensive C] {ι : Type u_1}
  [Finite ι] {F : CategoryTheory.Functor (CategoryTheory.Discrete ι) C} {c : CategoryTheory.Limits.Cocone F}
  (hc : CategoryTheory.Limits.IsColimit c) (i : CategoryTheory.Discrete ι) {X : C}
  (g : X ⟶ ((CategoryTheory.Functor.const (CategoryTheory.Discrete ι)).obj c.pt).obj i),
  CategoryTheory.Limits.HasPullback g (c.ι.app i)

Defined in

Mathlib.CategoryTheory.Extensive

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.FinitaryPreExtensiveFinite