Timeline for Why are monads useful?
Current License: CC BY-SA 3.0
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| Dec 28, 2011 at 14:46 | comment | added | Thomas Nevins | Just to amplify on Justin's answer slightly: the natural "geometric function theories" in algebraic geometry, i.e. categories of quasicoherent or coherent sheaves, categories of D-modules, categories of $\ell$-adic sheaves, etc. come with direct and inverse image functors of various kinds that have adjoints on one side or another. So one naturally has (co)monadic structure from that---I personally view this as a fundamental organizing principle. There are then many ways to play descent-type games in this setting; a very powerful recent tool is Lurie's Barr-Beck theorem for $\infty$-cats. | |
| Dec 26, 2011 at 14:02 | vote | accept | Lukas | ||
| Dec 26, 2011 at 14:46 | |||||
| Dec 26, 2011 at 13:32 | history | answered | Justin Noel | CC BY-SA 3.0 |