Theorems · Theorem · category theory

CategoryTheory.leftAdjoint_preservesTerminal_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) [inst_2 : CategoryTheory.Reflective R],
  CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete PEmpty.{v + 1})
    (CategoryTheory.monadicLeftAdjoint R)

The reflector always preserves terminal objects. Note this in general doesn't apply to any other limit.

Defined in

Mathlib.CategoryTheory.Monad.Limits

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Reflective