Theorems · Definition · category theory
CommMonCat.coyonedaType
CategoryTheory.Functor Type uᵒᵖ (CategoryTheory.Functor CommMonCat CommMonCat)
The Hom bifunctor sending a type X and a commutative monoid M to the commutative monoid
X → M with pointwise operations.
This is also the coyoneda embedding of Type into CommMonCat-valued presheaves of commutative
monoids.
- Defined in
- Mathlib.Algebra.Category.MonCat.Yoneda
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.unopproof · cited by 903
- MonoidHom.compproof · cited by 469
- CommMonCatstatement and proof · cited by 51
- CommMonCat.carrierproof · cited by 44
- CommMonCat.Hom.homproof · cited by 20
- CommMonCat.ofproof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- CommMonCat.coyonedaType_map_appstatement and proof · cited by 0
- CommMonCat.coyonedaType_obj_mapstatement and proof · cited by 0
- CommMonCat.coyonedaType_obj_obj_coestatement and proof · cited by 0