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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[coherent (infinity,1)-operad]]

   stub for coherent (infinity,1)-operad

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexmentioned some of the examples.

   mentioned some of the examples.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeMay 3rd 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItex> whose modules over $\mathcal{O}$-algebras Modules over algebras over operad ??

   whose modules over $\mathcal{O}$-algebras

   Modules over algebras over operad ??

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 3rd 2011
   • (edited May 3rd 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexSorry, what's the question? There is an operad $\mathcal{O}$, there is an $\mathcal{O}$-algebra $A$ and a category $A Mod$ of $A$-modules. Lurie calls $\mathcal{O}$ "coherent" if for all $A$ the $\infty$-category $A Mod$ is nice (has a well behaved tensor product)

   Sorry, what’s the question?

   There is an operad $\mathcal{O}$, there is an $\mathcal{O}$-algebra $A$ and a category $A Mod$ of $A$-modules. Lurie calls $\mathcal{O}$ “coherent” if for all $A$ the $\infty$-category $A Mod$ is nice (has a well behaved tensor product)

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeMay 3rd 2011
   • (edited May 3rd 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt is amazing that the structure would induce the *tensor product* two levels up, not one level up, what was my first guess of the meaning. (first level algebras over operads, second algebras over algebras... so to speak) In Hopf algebras the coproduct on Hopf algebra induces rigid monoidal structure on the category of usual modules over Hopf algebras. So this thing here is very different... P.S. why is it called "coherent" ?

   It is amazing that the structure would induce the tensor product two levels up, not one level up, what was my first guess of the meaning. (first level algebras over operads, second algebras over algebras… so to speak) In Hopf algebras the coproduct on Hopf algebra induces rigid monoidal structure on the category of usual modules over Hopf algebras. So this thing here is very different…

   P.S. why is it called “coherent” ?

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeMay 3rd 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItex> P.S. why is it called "coherent" ? That was my question too!

   P.S. why is it called “coherent” ?

   That was my question too!

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMay 4th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI don't know, I am not aware of an explanation of the choice of term. Just some term. Make a suggestion for how to rather call it.

   I don’t know, I am not aware of an explanation of the choice of term. Just some term. Make a suggestion for how to rather call it.

8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeMay 5th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexHmm, well, a *commutative theory*, or *monoidal monad*, is one whose algebras come with a tensor product. Since this is "an extra level up", as Zoran says, maybe something like "locally commutative" or "locally monoidal"?

   Hmm, well, a commutative theory, or monoidal monad, is one whose algebras come with a tensor product. Since this is “an extra level up”, as Zoran says, maybe something like “locally commutative” or “locally monoidal”?

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeMay 5th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat sounds good. I have changed the page name to [[locally monoidal (infinity,1)-operad]].

   That sounds good. I have changed the page name to locally monoidal (infinity,1)-operad.