Theorems · Definition · category theory

CategoryTheory.IsFiltered.SmallFilteredIntermediate

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.IsFilteredOrEmpty C] →
      {D : Type u₁} → [inst_2 : CategoryTheory.Category.{v₁, u₁} D] → CategoryTheory.Functor D C → Type (max u₁ v)

Every functor from a small category to a filtered category factors fully faithfully through a small filtered category. This is that category.

Defined in

Mathlib.CategoryTheory.Filtered.Small

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsFilteredOrEmptyCategoryTheory.Category