According to an off-hand comment in page 4 of Leinster's "Up-to-Homotopy Monoids", differential graded algebras are just monoid objects in the monoidal category of chain complexes. The definition of the monoidal structure on that category (i.e. the tensor product of chain complexes) is kind of daunting, though, still. I sort of get the definition of objects, but I don't deeply grok the sign alternation in the definition of the boundary maps — why does it depend on just i and not j?
