Theorems · Theorem · category theory

CategoryTheory.FinallySmall.preservesColimitsOfShape_of_isFiltered

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsFiltered C]
  [CategoryTheory.LocallySmall.{w, v, u} C] [CategoryTheory.FinallySmall C] {D : Type u_1} {E : Type u_2}
  [inst_4 : CategoryTheory.Category.{v_1, u_1} D] [inst_5 : CategoryTheory.Category.{v_2, u_2} E]
  (F : CategoryTheory.Functor D E) [CategoryTheory.Limits.PreservesFilteredColimitsOfSize.{w, w, v_1, v_2, u_1, u_2} F],
  CategoryTheory.Limits.PreservesColimitsOfShape C F

Defined in

Mathlib.CategoryTheory.Filtered.FinallySmall

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsFilteredCategoryTheory.LocallySmallCategoryTheory.FinallySmallCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesFilteredColimitsOfSize