Theorems · Definition · category theory
CategoryTheory.algebraEquivUnder
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(X : C) →
[inst_1 : CategoryTheory.Limits.HasBinaryCoproducts C] →
(CategoryTheory.coprodMonad X).Algebra ≌ CategoryTheory.Under XThe equivalence from algebras for the coproduct monad to the under category.
- Defined in
- Mathlib.CategoryTheory.Monad.Products
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Under.rightproof · cited by 128
- CategoryTheory.Monad.Algebrastatement and proof · cited by 110
- CategoryTheory.Limits.HasBinaryCoproductsstatement and proof · cited by 98
- CategoryTheory.Monad.Algebra.Aproof · cited by 81
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Under.costarAdjForgetproof · cited by 0
- CategoryTheory.algebraEquivUnder_counitIsostatement and proof · cited by 0
- CategoryTheory.algebraEquivUnder_functorstatement and proof · cited by 0
- CategoryTheory.algebraEquivUnder_inversestatement and proof · cited by 0
- CategoryTheory.algebraEquivUnder_unitIsostatement and proof · cited by 0