Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesColimitsOfSize.preservesFiniteColimits

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [CategoryTheory.Limits.PreservesColimitsOfSize.{w, w₂, v₁, v₂, u₁, u₂} F],
  CategoryTheory.Limits.PreservesFiniteColimits F

If we preserve colimits of some arbitrary size, then we preserve all finite colimits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Finite

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitsOfSize