Theorems · Theorem · category theory

CategoryTheory.FinitaryExtensive.isPullback_initial_to

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.FinitaryExtensive 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 j : CategoryTheory.Discrete ι),
  i ≠ j →
    CategoryTheory.IsPullback (CategoryTheory.Limits.initial.to (F.obj i)) (CategoryTheory.Limits.initial.to (F.obj j))
      (c.ι.app i) (c.ι.app j)

Defined in

Mathlib.CategoryTheory.Extensive

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.FinitaryExtensiveFinite