Timeline for What is a homotopy between $L_\infty$-algebra morphisms
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6 events
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| Aug 13, 2013 at 23:03 | comment | added | Urs Schreiber | What I wrote back then was uninformed of homotopy theory. I wish somebody back then had pointed me to the homotopy theory. Most of it was already known. It's much more fun to play with formulas if you know what you are doing and are not just guessing and fiddling around. :-) | |
| Aug 13, 2013 at 23:02 | comment | added | Urs Schreiber | I am just saying the equations that you need are those for a path space object in your preferred model. A fully explicit construction is in Dolgushev's note that I pointed to. Did you have a look? This typically comes down to the kind of construction Theo mentions, but has the advantage that you actually know that it is the right thing. | |
| Aug 13, 2013 at 12:26 | comment | added | Mark.Neuhaus | I'll consider the Sullivan Construction, Theo gave, as pretty doable to get actual equations for $n$-morphisms, at least for lower $n$. What would you say is, from a compuational POV, another good way to proceed? | |
| Aug 13, 2013 at 12:19 | comment | added | Mark.Neuhaus | Ok. I understand that you gave me the big picture, or to say a hole bunch of big pictures, all equivalent in the $(\infty,1)$-sense. But still from having a model structure, or a homotopy structure, it is a long way to actual equations. I never did the hammock process or things like that, but it really looks like a lot of work. In your n-cat post from 2006 you had the same desire for explicit $n$-morpism equation. So did you succeed or (if not) what was the reason to break on that? -Maybe explicit equations are too involved and you decided, that nowing their existence is enough for your work? | |
| Aug 12, 2013 at 12:21 | history | edited | Urs Schreiber | CC BY-SA 3.0 |
added 13 characters in body
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| Aug 12, 2013 at 7:02 | history | answered | Urs Schreiber | CC BY-SA 3.0 |