Theorems · Theorem · category theory

CategoryTheory.Limits.Concrete.small_sections_of_hasLimit

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : outParam (C → C → Type u_1)} {CC : outParam (C → Type v)}
  [inst_1 : outParam ((X Y : C) → FunLike (FC X Y) (CC X) (CC Y))] [inst_2 : CategoryTheory.ConcreteCategory C FC]
  [(CategoryTheory.forget C).IsCorepresentable] {J : Type w} [inst_4 : CategoryTheory.Category.{t, w} J]
  (G : CategoryTheory.Functor J C) [CategoryTheory.Limits.HasLimit G],
  Small.{v, max v w} ↑(G.comp (CategoryTheory.forget C)).sections

If a functor G : J ⥤ C to a concrete category has a limit and that forget C is corepresentable, then (G ⋙ forget C).sections is small.

Defined in

Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryoutParamCategoryTheory.ConcreteCategoryCategoryTheory.Functor.IsCorepresentableCategoryTheory.CategoryCategoryTheory.Limits.HasLimit