Theorems · Theorem · category theory

CategoryTheory.Limits.preservesColimitsOfSize_of_univLE

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

A functor preserving larger colimits also preserves smaller colimits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryUnivLEUnivLECategoryTheory.Limits.PreservesColimitsOfSize