Definition

An algebra over an operad is the single hom-object of a category over an operad which has a single object.

Remarks

• If $C$ is the symmetric monoidal enriching category, $O$ the $C$-enriched operad in question, and $A\in \mathrm{Obj}(C)$ is the single hom-object of the O-category with single object, it makes sense to write $BA$ for that $O$-category. Compare the discussion at monoid and group, which are special cases of this.