most recent 30 from http://mathoverflow.net 2013-05-24T07:21:37Z http://mathoverflow.net/feeds/question/17468 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17468/derivators-in-english Harry Gindi 2010-03-08T13:14:34Z 2011-09-09T06:42:40Z

<p>Grothendieck, before he disappeared, was working on a manuscript called "Les Derivateurs", which detailed the theory of derivators. Prof. Cisinski has done work with them as he mentioned in this <a href="http://mathoverflow.net/questions/17425/homotopy-limits-over-fibered-categories/17463#17463" rel="nofollow">post</a>. However, most of his work is in French, and I was wondering if there are any typed up references in english (the nLab has written notes from a seminar, but that's it). I intend to read the references in French later, but could someone explain or give a reference that explains in English the definition of a derivator and the motivation for them? </p>

http://mathoverflow.net/questions/17468/derivators-in-english/17470#17470 Peter Arndt 2010-03-08T13:33:00Z 2010-03-08T17:07:35Z

<p>Some very brief remarks on derivateurs are in Bertrand Toen's habilitation thesis on pages 12-14 and 27-29, available <a href="http://www.math.univ-toulouse.fr/~toen/note.html" rel="nofollow">here</a>. They mainly emphasize how derivateurs are sort of a 2-truncated homotopy theory of homotopy theories - nothing to learn derivateur-language from, but maybe a nice addition to the general picture.</p>

http://mathoverflow.net/questions/17468/derivators-in-english/17502#17502 Lennart Meier 2010-03-08T18:51:53Z 2010-03-08T18:51:53Z

<p>A theory of a very similar flavour can be found in a <a href="http://www.mathematik.uni-osnabrueck.de/K-theory/0139/Adams.pdf" rel="nofollow">preprint</a> of Jens Franke.</p>

http://mathoverflow.net/questions/17468/derivators-in-english/17562#17562 Harry Gindi 2010-03-09T01:39:59Z 2010-03-09T01:39:59Z

<p>Urs Schreiber updated the <a href="http://ncatlab.org/nlab/show/derivator" rel="nofollow">nLab page</a> 40 minutes or so ago with an explanation from Prof. Cisinski.</p>

http://mathoverflow.net/questions/17468/derivators-in-english/17589#17589 Denis-Charles Cisinski 2010-03-09T10:04:54Z 2010-03-09T10:04:54Z

<p>For a few references in English, there are the papers of Heller, the main one being:</p> <p>A. Heller, Homotopy theories, Mem. Amer. Math. Soc. 71 (383) (1988)</p> <p>There is also a paper I wrote with A. Neeman, in which there is a little introduction to derivators in the second half of: Additivity for derivator K-theory, Adv. Math. 217 (2008), no. 4, 1381-1475</p> <p>One can see derivators in action in the work of G. Tabuada (he explains Bousfield localization and stabilization in this setting, and compares with the model category point of view): Higher K-theory via universal invariants, Duke Math. J. 145 (2008), no. 1, 121–206 (availabe as arXiv:0706.2420).</p>

http://mathoverflow.net/questions/17468/derivators-in-english/17600#17600 Zoran Škoda 2010-03-09T12:37:52Z 2010-03-09T12:37:52Z

<p>George Maltsiniotis has given a mini-course in Seville last year, they include some handwritten notes in English, which are the part 3 of the course:</p> <p><a href="http://people.math.jussieu.fr/~maltsin/Seville/Lecture_III_Derivators.pdf" rel="nofollow">Lecture_III_Derivators.pdf</a></p> <p>For the other parts of the course notes see the conference <a href="http://congreso.us.es/htag09/php/index.php?carga=courses" rel="nofollow">page</a>.</p>

http://mathoverflow.net/questions/17468/derivators-in-english/74979#74979 Beren Sanders 2011-09-09T06:42:40Z 2011-09-09T06:42:40Z

<p>My recommendation would be <a href="http://www.math.uni-bonn.de/~mgroth/" rel="nofollow">Moritz Groth</a>'s excellent notes</p> <ul> <li><a href="http://www.math.uni-bonn.de/~mgroth/groth_derivators.pdf" rel="nofollow">Derivators, pointed derivators, and stable derivators</a>.</li> </ul> <p>He also has a follow-up paper on</p> <ul> <li><a href="http://www.math.uni-bonn.de/~mgroth/groth_monoidal.pdf" rel="nofollow">Monoidal and Enriched derivators</a></li> </ul> <p>as well as a</p> <ul> <li><a href="http://www.math.uni-bonn.de/~mgroth/InfinityCategories.pdf" rel="nofollow">A short course on infinity-categories</a>.</li> </ul> <p>These are great introductions to all of these topics.</p>