| K-Vect | Set |
|---|
| Given a field (or commutative ring) K, the category K-Vect is a symmetric monoidal category with product ⊗ and identity K. |
The category Set is a symmetric monoidal category with product × and identity {*}. |
| A unital associative algebra is an object of K-Vect together with morphisms and satisfying |
Any object of Set, S has two unique morphisms and satisfying . In particular, ε is unique because {*} is a terminal object. |
| A coalgebra is an object B with morphisms and satisfying . |
A monoid is an object M together with morphisms and satisfying . |