# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 8th 2010

in preparation of the next session of our Seminar on derived differential geometry I am starting

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeNov 8th 2010

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 8th 2010

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 :-)

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeNov 8th 2010

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.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 8th 2010

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.