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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded statement of and references to the weak equivalence with the Fulton-MacPherson operad ([here](https://ncatlab.org/nlab/show/little+cubes+operad#RelationToFultonMacPhersonOperad)) added the same statement also at _[[Fulton-MacPherson operad]]_ <a href="https://ncatlab.org/nlab/revision/diff/little+cubes+operad/32">diff</a>, <a href="https://ncatlab.org/nlab/revision/little+cubes+operad/32">v32</a>, <a href="https://ncatlab.org/nlab/show/little+cubes+operad">current</a>

   added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

   added the same statement also at Fulton-MacPherson operad

   diff, v32, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 3rd 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded redirects: E_n-operad <a href="https://ncatlab.org/nlab/revision/diff/little+cubes+operad/40">diff</a>, <a href="https://ncatlab.org/nlab/revision/little+cubes+operad/40">v40</a>, <a href="https://ncatlab.org/nlab/show/little+cubes+operad">current</a>

   Added redirects: E_n-operad

   diff, v40, current

3. • CommentRowNumber3.
   • CommentAuthorHurkyl
   • CommentTimeNov 18th 2021
   • (edited Nov 18th 2021)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexThe statement that $Rect(\square^k \times S, \square^k )$ can be identified with an open subset of $(\mathbb{R}^{2k})^S$ is wrong, isn't it? For example, $Rect(\square^1, \square^1)$ can be identified with the set of pairs $(a,b)$ satisfying $0 \lt a \leq 1$, $|b| \leq 1-a$, which is a triangle that includes part of its boundary.

   The statement that $Rect(\square^k \times S, \square^k )$ can be identified with an open subset of $(\mathbb{R}^{2k})^S$ is wrong, isn’t it?

   For example, $Rect(\square^1, \square^1)$ can be identified with the set of pairs $(a,b)$ satisfying $0 \lt a \leq 1$, $|b| \leq 1-a$, which is a triangle that includes part of its boundary.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 19th 2021
   • (edited Nov 19th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI suppose this is about [this Definition](https://ncatlab.org/nlab/show/little+cubes+operad#DefinitionViaRectilinearEmbeddings) (which, somewhat awkwardly, somebody had copied verbatim from HA [p. 758](https://www.math.ias.edu/~lurie/papers/HA.pdf#page=758); I have now at least added some hyperlinks and touched the formatting and wording). <a href="https://ncatlab.org/nlab/revision/diff/little+cubes+operad/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/little+cubes+operad/41">v41</a>, <a href="https://ncatlab.org/nlab/show/little+cubes+operad">current</a>

   I suppose this is about this Definition (which, somewhat awkwardly, somebody had copied verbatim from HA p. 758; I have now at least added some hyperlinks and touched the formatting and wording).

   diff, v41, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 19th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexRegarding the point you raise: Scanning through *Higher Algebra*, it looks like the identity map is meant to count as a rectilinear embedding (explicit in Ex. 5.1.0.6, [p. 759](https://www.math.ias.edu/~lurie/papers/HA.pdf#page=759)), while would-be open-ness of the space of rectilinear embedding seems not to be used. That makes me think that the "open subset" on p. 758 is a glitch and that the line was just meant to say that $Rect(-,-)$ is equipped with the subspace topology.

   Regarding the point you raise: Scanning through Higher Algebra, it looks like the identity map is meant to count as a rectilinear embedding (explicit in Ex. 5.1.0.6, p. 759), while would-be open-ness of the space of rectilinear embedding seems not to be used. That makes me think that the “open subset” on p. 758 is a glitch and that the line was just meant to say that $Rect(-,-)$ is equipped with the subspace topology.

6. • CommentRowNumber6.
   • CommentAuthorHurkyl
   • CommentTimeNov 19th 2021
   • (edited Nov 19th 2021)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexOh good; I'm not missing something and it's harmless. Since I've just started trying to digest the little cubes operad and still find it somewhat opaque I really didn't feel confident just removing that line.

   Oh good; I’m not missing something and it’s harmless. Since I’ve just started trying to digest the little cubes operad and still find it somewhat opaque I really didn’t feel confident just removing that line.