Timeline for What non-categorical applications are there of homotopical algebra?
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| Jun 9, 2014 at 23:07 | comment | added | David Ben-Zvi | @JasonPolak: I wrote something of that flavor here: mathoverflow.net/questions/84381/… - the short of it is, $\infty$ categories are perfectly suited to make formal arguments that ought to be formal. It is not a computationally effective language but one that powerfully captures the "pure thought" aspects of algebra: if you're naive about homotopy theory (like me) you can still easily prove analogs of statements that are true for robust structural reasons in a discrete setting, using these tools. A favorite example: cf. Barr-Beck-Lurie theorem. | |
| Jun 8, 2014 at 1:00 | comment | added | user1437 | Nice answer. I was wondering if you could briefly explain the point "The ∞-language in my mind is just a very convenient and relatively friendly apparatus to understand, navigate and apply this theory." Specifically, how does the language of infinity categories make it easier to apply homotopical algebra? | |
| Jun 6, 2014 at 23:28 | comment | added | David Ben-Zvi | I'd have liked to add something intelligent about algebraic K-theory and its triumphs as applications of homotopical algebra but can't pretend to do it justice - though I can link here. | |
| S Jun 6, 2014 at 23:14 | history | answered | David Ben-Zvi | CC BY-SA 3.0 | |
| S Jun 6, 2014 at 23:14 | history | made wiki | Post Made Community Wiki by David Ben-Zvi |