most recent 30 from http://mathoverflow.net 2013-06-20T00:53:43Z http://mathoverflow.net/feeds/question/95118 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95118/algebraic-vs-topological-study-of-deformations-deformation-stacks-vs-topolog s.barmeier 2012-04-25T05:41:07Z 2012-04-25T05:41:07Z

<p>In my limited understanding, one can always find a category that captures the data of a deformation problem. But for a given deformation problem with a topologized deformation space, is there any advantage of reinterpreting it in the language of category theory (stacks? fibered categories? descent theory? Grothendieck topologies?)?</p> <p>I guess, I am wondering if the answer might be "Hey, if you have a topological space already, why do you need a deformation category?", or if there is a kind of formalism that does help to answer the deformation problem more wholly or more naturally than the approach using tools from general topology.</p> <p>Has Teichmüller theory been interpreted in the language of category theory, or is that a problem that is either impossible or just trivial and unnecessary?</p>