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Theorems · Theorem · category theory

CategoryTheory.hasColimits_of_reflective

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (R : CategoryTheory.Functor D C) [CategoryTheory.Reflective R]
  [CategoryTheory.Limits.HasColimitsOfSize.{v, u, v₁, u₁} C], CategoryTheory.Limits.HasColimitsOfSize.{v, u, v₂, u₂} D

If C has colimits then any reflective subcategory has colimits.

Defined in
Mathlib.CategoryTheory.Monad.Limits
Cited by
1 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ReflectiveCategoryTheory.Limits.HasColimitsOfSize
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CategoryTheory.Adjunction.isCardinalLocallyPresentable · cited by 2Adjunction.isCardinalLoca…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Limits.HasColimitsOfSize · cited by 124Limits.HasColimitsOfSizeCategoryTheory.Reflective · cited by 27CategoryTheory.ReflectiveCategoryTheory.hasColimitsOfShape_of_reflective · cited by 2CategoryTheory.hasColimit…CategoryTheory.hasColimits_of…CITED BYCITES

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