Main Page | See live article | Alphabetical index 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 . This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.