Algebraic Systems As Monoidal Functor Categories

An algebraic system consists of sets with operations satisfying some relations. This is broad enough to include the usual systems such as groups, rings, modules, group representations, etc. Any algebraic structure can be regarded as a strict small monoidal category generated by a graph with some relations between arrows and an algebraic system as a category is equivalent to the monoidal functor category from such strict small monoidal category to any underlying monoidal category such as (Set, ×,*) and (hTop_*,∧,*).