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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: Markdowncreated stub for [[E-k-operad]]

   created stub for E-k-operad

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: TobyBartels
   Format: MarkdownI think that the name should be [[E-k operad]] (which you already made a redirect); more generally, it should be ‘<latex>E_k</latex> operad’, not ‘<latex>E_k</latex>-operad’. Compare: an ‘<latex>E_k</latex>-ring’ is like a monoid but different, because it's been hit with this <latex>E_k</latex> thing. But that's not what we have here; the <latex>E_k</latex> operad *is* an operad, and it hasn't been hit with any <latex>E_k</latex> thing; it *is* the <latex>E_k</latex> thing. Am I right?

   I think that the name should be E-k operad (which you already made a redirect); more generally, it should be ‘ operad’, not ‘-operad’. Compare: an ‘-ring’ is like a monoid but different, because it's been hit with this thing. But that's not what we have here; the operad is an operad, and it hasn't been hit with any thing; it is the thing.

   Am I right?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI see, good point. I haven't thought much about this. But, right, it's the operad named <latex> E_k </latex>, of course. Have changed the page name now.

   I see, good point. I haven't thought much about this. But, right, it's the operad named , of course.

   Have changed the page name now.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: TobyBartels
   Format: MarkdownShould [[E-infinity operad]] redirect there too, or does it get its own page?

   Should E-infinity operad redirect there too, or does it get its own page?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownEventually it should probably have its own page. Maybe at the moment it would be more convenient to have a redirect. Also the E-1 operad aka Ass should eventually get its own page. And maybe E-2 and E-3. And E-oo. n and one-two-three-infinity. As with n-categories.

   Eventually it should probably have its own page. Maybe at the moment it would be more convenient to have a redirect.

   Also the E-1 operad aka Ass should eventually get its own page. And maybe E-2 and E-3. And E-oo. n and one-two-three-infinity. As with n-categories.

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: TobyBartels
   Format: Markdown>n and one-two-three-infinity. As with n-categories. Now you know my next question: Is there an <latex>E_0</latex> operad?

   n and one-two-three-infinity. As with n-categories.

   Now you know my next question:

   Is there an operad?

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI suppose that's the trivial operad. The terminal operad. Now I foretell your next question...

   I suppose that's the trivial operad. The terminal operad.

   Now I foretell your next question...

8. • CommentRowNumber8.
   • CommentAuthorEric
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Eric
   Format: Text:D

   :D
9. • CommentRowNumber9.
   • CommentAuthorMike Shulman
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownI don't think it's really accurate to talk about *the* <latex>E_k</latex> operad. I always thought that one talked about *an* <latex>E_k</latex> operad, of which the little k-cubes operad is just the most common example. For instance, there is the little k-disks operad. And in the cases k=1 and <latex>\infty</latex> there are lots more <latex>E_k</latex> operads; for instance, the linear isometries operad is <latex>E_\infty</latex>.

   I don't think it's really accurate to talk about the operad. I always thought that one talked about an operad, of which the little k-cubes operad is just the most common example. For instance, there is the little k-disks operad. And in the cases k=1 and there are lots more operads; for instance, the linear isometries operad is .

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009
    • (edited Nov 11th 2009)
    • PermaLink
    Author: Urs
    Format: MarkdownRight, i thought about that but then was being lazy. I need to polish the terminology. I might have been, as you may have noticed, under the influence of Lurie's latest. He writes <latex> \mathbb{E}[k] </latex> specifically for the little cubes thingy. I am not sure, what should be the pattern here? Is the blackboard-boldface to be read as indicating that little cubes are meant?

    Right, i thought about that but then was being lazy. I need to polish the terminology. I might have been, as you may have noticed, under the influence of Lurie's latest. He writes specifically for the little cubes thingy.

    I am not sure, what should be the pattern here? Is the blackboard-boldface to be read as indicating that little cubes are meant?

11. • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeNov 12th 2009
    • PermaLink
    Author: Mike Shulman
    Format: MarkdownFar be it from me to claim to understand Lurie's notation and terminology. Peter May writes <latex>\mathscr{C}_n</latex> for the little n-cubes operad (<latex>\mathscr{C}</latex> for "cubes"?).

    Far be it from me to claim to understand Lurie's notation and terminology. Peter May writes for the little n-cubes operad ( for "cubes"?).