Theorems · Theorem · category theory

CategoryTheory.isRightAdjoint_triangle_lift_monadic

∀ {A : Type u₁} {B : Type u₂} {C : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} A]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} B] [inst_2 : CategoryTheory.Category.{v₃, u₃} C]
  (U : CategoryTheory.Functor B C) [CategoryTheory.MonadicRightAdjoint U] {R : CategoryTheory.Functor A B}
  [CategoryTheory.Limits.HasReflexiveCoequalizers A] [(R.comp U).IsRightAdjoint], R.IsRightAdjoint

If R ⋙ U has a left adjoint, the domain of R has reflexive coequalizers and U is a monadic functor, then R has a left adjoint. This is a special case of isRightAdjoint_triangle_lift which is often more useful in practice.

Defined in

Mathlib.CategoryTheory.Adjunction.Lifting.Left

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonadicRightAdjointCategoryTheory.Limits.HasReflexiveCoequalizersCategoryTheory.Functor.IsRightAdjoint