Theorems · Theorem · category theory

CategoryTheory.hasLimit_of_created

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] (K : CategoryTheory.Functor J C)
  (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.HasLimit (K.comp F)] [CategoryTheory.CreatesLimit K F],
  CategoryTheory.Limits.HasLimit K

If F creates the limit of K and K ⋙ F has a limit, then K has a limit.

Defined in

Mathlib.CategoryTheory.Limits.Creates

Cited by

9 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitCategoryTheory.CreatesLimit