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in preparation of the next session of our Seminar on derived differential geometry I am starting
Is there a reason to put ∞- in front of “algebra” here and at other similar places? Is there any other sort of algebra over an (∞,1)-operad? We don’t talk about “2-algebras” for 2-monads.
Hm, you think i should change it? It’s somewhat redundant, true, but not entirely without purpose. There is a sensible notion of $n$-algebra over a $k$-operad/monad for independent $n,k$.
But I am not dogmatic about this. Just feeling a bit lazy now to change it all :-)
There is a sensible notion of $n$-algebra over a $k$-operad/monad for independent $n,k$.
Such that a 2-algebra over the 1-operad for monoids is a monoidal category, for instance? I guess. That doesn’t seem like a really important reason to keep the prefix for everything else; maybe we could just say that the prefix isn’t really necessary here, but could be used to disambiguate elsewhere.
Such that a 2-algebra over the 1-operad for monoids is a monoidal category, for instance?
For instance. Maybe more importantly, such that $\infty$-algebras over the 1-operads $Ass$, $Comm$ are $A_\infty$-algebras, $E_\infty$-algebras, etc.
But, as I said, I can live well with dropping that prefix. I will eventually do so.
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