>>13965262OK, I can try but I'm still a bit of a noob myself with these -algebras (or Awoo-algebras as a friend of mine calls them ), so please don't hate me if some details are only almost there...
So we start with some field and take some graded -vector space , and then we want to have morphisms and (this to make an equation coming up actually sensible), of degrees each. Now, take your favourite and consider all integral partitions with . This will then give us the sum over such partitions and we require . If this is satisfied for every , we have an -algebra. Also, observe that by the equation, so is a DG vector space over our field!!!!
As with those -morphisms, a morphism of -algebras will come with its components and they will have their degree stuff and some awful composition formula (the sign stuff related to that is !!!!), which I'll skip because blergh... But the importance is that will be the one with the meaningful interaction with our differential , and so is a quasi-isomorphism of these infinity thingies iff is a quasi-iso in the usual sense (definition, not a result!).
