Theorems · Definition · category theory

CategoryTheory.FinallySmall.FilteredFinalModel

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.IsFiltered C] → [CategoryTheory.LocallySmall.{w, v, u} C] → [CategoryTheory.FinallySmall C] → Type w

If C is a locally small filtered finally small category, this is a small filtered category, equipped with a final functor to C (see fromFilteredFinalModel).

Defined in: Mathlib.CategoryTheory.Filtered.FinallySmall
Cited by: 0 results in Mathlib
Foundations: Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsFiltered CategoryTheory.LocallySmall CategoryTheory.FinallySmall

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.LocallySmallstatement and proof · cited by 242
CategoryTheory.IsFilteredstatement and proof · cited by 210
CategoryTheory.FinallySmallstatement and proof · cited by 16
CategoryTheory.FinallySmall.exists_of_isFilteredproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.FinallySmall.fromFilteredFinalModelstatement · cited by 2