Theorems · Theorem · category theory

CategoryTheory.Comonad.forget_creates_limits_of_comonad_preserves

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : Type u} [inst_1 : CategoryTheory.Category.{v, u} J]
  {T : CategoryTheory.Comonad C} [CategoryTheory.Limits.PreservesLimitsOfShape J T.toFunctor]
  (D : CategoryTheory.Functor J T.Coalgebra) [CategoryTheory.Limits.HasLimit (D.comp T.forget)],
  CategoryTheory.Limits.HasLimit D

For D : J ⥤ Coalgebra T, D ⋙ forget T has a limit, then D has a limit provided limits of shape J are preserved by T.

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.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.HasLimit