Timeline for Why are operads useful?
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| Aug 10, 2011 at 15:27 | comment | added | Ryan Budney | @Mark: I think the why is at least partially addressed by the braid groups example. One way to look at groups is they act on things. But in this instance, the classifying spaces of pure braid groups is itself an "actor" -- acting on configuration spaces -- but acting in an operadic sense. So there's a type of higher symmetry among braid groups that the operad is catching. In algebraic topology universal algebras come up quite often -- things like algebras of cohomology operations. Cohomology as a module over these algebras are a more powerful object than just cohomology rings. | |
| Aug 10, 2011 at 8:36 | comment | added | user6976 | @Ryan: Your answer is mostly about "what" rather than "why". Right? For example, why would anybody need a "category-independent notion of universal algebra" (and what does it mean exactly)? | |
| Aug 9, 2011 at 19:15 | history | answered | Ryan Budney | CC BY-SA 3.0 |