Theorems · Definition · category theory

CategoryTheory.Limits.PreservesFilteredColimits

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → Prop

A functor is said to preserve filtered colimits, if it preserves all colimits of shape J, where J is a filtered category which is small relative to the universe in which morphisms of the source live.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Filtered

Cited by

35 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category