Theorems · Theorem · category theory

CategoryTheory.hasLimits_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.Limits.HasLimitsOfSize.{v, u, v₁, u₁} C]
  [CategoryTheory.Reflective R], CategoryTheory.Limits.HasLimitsOfSize.{v, u, v₂, u₂} D

If C has limits then any reflective subcategory has limits.

Defined in: Mathlib.CategoryTheory.Monad.Limits
Cited by: 0 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Limits.HasLimitsOfSize CategoryTheory.Reflective

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Limits.HasLimitsOfSizestatement and proof · cited by 71
CategoryTheory.Reflectivestatement and proof · cited by 27
CategoryTheory.hasLimitsOfShape_of_reflectiveproof · cited by 2

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