Theorems · Theorem · category theory

CategoryTheory.rightAdjoint_preservesInitial_of_coreflective

∀ {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.Coreflective R],
  CategoryTheory.Limits.PreservesColimitsOfShape (CategoryTheory.Discrete PEmpty.{v + 1})
    (CategoryTheory.comonadicRightAdjoint R)

The coreflector always preserves initial objects. Note this in general doesn't apply to any other colimit.

Defined in

Mathlib.CategoryTheory.Monad.Limits

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Coreflective