Timeline for Is an A-infinity thing the same the same as strict thing viewed through a homotopy equivalence?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2014 at 0:18 | answer | added | Peter May | timeline score: 6 | |
| Nov 24, 2014 at 18:19 | answer | added | Dmitri Pavlov | timeline score: 3 | |
| Jul 23, 2014 at 8:55 | history | edited | David White | CC BY-SA 3.0 |
Fixed typos, including in title
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| Jan 19, 2011 at 6:41 | answer | added | jeff smith | timeline score: 6 | |
| Jan 13, 2011 at 17:30 | comment | added | aleph0 | @Clark: I think that is indeed what I am asking. I am thinking of A_\infty as up-to-coherent-homotopy monoid/group/algebra/..., but I am trying to get a better feel of what exactly that means. It would be nice to be able to think that this was a strict (up-to-identity) monoid/... smudged by a homotopy equivalence. My question thus has two parts: (1) if I have a strict structure and smudge it through a homotopy equivalence, do I get an A_\infty structure? (2) If I have an A_\infty structure, can I assume it arose in this way? | |
| Jan 12, 2011 at 14:13 | answer | added | Tyler Lawson | timeline score: 12 | |
| Jan 12, 2011 at 5:14 | answer | added | Ben Wieland | timeline score: 5 | |
| Jan 12, 2011 at 3:08 | comment | added | Mariano Suárez-Álvarez | @Tom: I guess the square is a place holder for arbitrary structures. For example, it could stand for "boolean algebra". I wonder if boolean-algebras-up-to-coherent-homotopy ever show up :) | |
| Jan 12, 2011 at 3:00 | answer | added | John Klein | timeline score: 16 | |
| Jan 11, 2011 at 22:56 | comment | added | Tom Goodwillie | @Theo: What does the "square" symbol stand for? @Clark: I think that that is exactly what he is asking. And I don't know the answer, even in the case of spaces, except in the case when the monoid of components of the space is a group. | |
| Jan 11, 2011 at 22:23 | comment | added | Theo Johnson-Freyd | I think your question is the following: "Is every $\Box_\infty$ space homotopy-equivalent to a strict $\Box$ space, for every value of $\Box$?" Is this right? | |
| Jan 11, 2011 at 21:37 | comment | added | Clark Barwick | I'm having trouble parsing your question. You can think of A_infty structures as up-to-coherent-homotopy monoid structures. But you may be asking something different. But I think you are asking whether, in any symmetric monoidal model category, an A_infty algebra can be strictified into a strict monoid structure. Is that right? | |
| Jan 11, 2011 at 19:26 | history | edited | aleph0 | CC BY-SA 2.5 |
fixed typo
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| Jan 11, 2011 at 17:27 | history | asked | aleph0 | CC BY-SA 2.5 |