Theorems · Definition · category theory

CategoryTheory.Limits.Types.limitEquivSections

{J : Type v} →
  [inst : CategoryTheory.Category.{w, v} J] →
    (F : CategoryTheory.Functor J (Type u)) →
      [inst_1 : CategoryTheory.Limits.HasLimit F] → CategoryTheory.Limits.limit F ≃ ↑F.sections

The equivalence between the abstract limit of F in Type max v u and the "concrete" definition as the sections of F.

Defined in

Mathlib.CategoryTheory.Limits.Types.Limits

Cited by

4 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasLimit