Theorems · Inductive type · category theory

CategoryTheory.CreatesLimit

{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] →
            CategoryTheory.Functor J C → CategoryTheory.Functor C D → Type (max (max (max (max u₁ u₂) v₁) v₂) w)

Definition 3.3.1 of [Riehl]. We say that F creates limits of K if, given any limit cone c for K ⋙ F (i.e. below) we can lift it to a cone "above", and further that F reflects limits for K. If F reflects isomorphisms, it suffices to show only that the lifted cone is a limit - see createsLimitOfReflectsIso.

Defined in

Mathlib.CategoryTheory.Limits.Creates

Cited by

6 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category