Theorems · Definition · category theory
AlgCat.free
(R : Type u) → [inst : CommRing R] → CategoryTheory.Functor (Type u) (AlgCat R)
The "free algebra" functor, sending a type S to the free algebra on S.
- Defined in
- Mathlib.Algebra.Category.AlgCat.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- AlgCatstatement · cited by 75
- FreeAlgebraproof · cited by 48
- FreeAlgebra.ιproof · cited by 28
- AlgCat.ofproof · cited by 23
- FreeAlgebra.liftproof · cited by 21
- AlgCat.ofHomproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- AlgCat.free_objstatement and proof · cited by 0
- AlgCat.adjstatement and proof · cited by 0
- AlgCat.free_mapstatement and proof · cited by 0