Theorems · Definition · category theory
CategoryTheory.algebraToUnder
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(X : C) →
[inst_1 : CategoryTheory.Limits.HasBinaryCoproducts C] →
CategoryTheory.Functor (CategoryTheory.coprodMonad X).Algebra (CategoryTheory.Under X)The forward direction of the equivalence from algebras for the coproduct monad to the under category.
- Defined in
- Mathlib.CategoryTheory.Monad.Products
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Understatement · cited by 276
- CategoryTheory.Limits.coprod.inlproof · cited by 137
- CategoryTheory.Monad.Algebrastatement and proof · cited by 110
- CategoryTheory.Limits.HasBinaryCoproductsstatement and proof · cited by 98
- CategoryTheory.Under.mkproof · cited by 65
- CategoryTheory.Monad.Algebra.Hom.fproof · cited by 48
- CategoryTheory.Monad.Algebra.aproof · cited by 45
- CategoryTheory.Under.homMkproof · cited by 43
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.algebraEquivUnderproof · cited by 4
- CategoryTheory.Under.costarproof · cited by 2
- CategoryTheory.algebraToUnder_mapstatement and proof · cited by 0
- CategoryTheory.algebraToUnder_objstatement and proof · cited by 0
- CategoryTheory.algebraEquivUnder_counitIsostatement · cited by 0
- CategoryTheory.algebraEquivUnder_functorstatement · cited by 0
- CategoryTheory.algebraEquivUnder_unitIsostatement · cited by 0