Geodesic
Homotopy colimits in stable representation theory
Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 331-360.

Voir la notice de l'article provenant de la source International Press of Boston

We study the problem of existence and uniqueness of homotopy colimits in stable representation theory, where one typically does not have model category structures to guarantee that these homotopy colimits exist or have good properties. We get both negative results (homotopy cofibers fail to exist if there exist any objects of positive finite projective dimension!) and positive results (reasonable conditions under which homotopy colimits exist and are unique, even when model category structures fail to exist). We describe some applications to Waldhausen $K$-theory and to deformation-theoretic methods in stable representation theory.
DOI : 10.4310/HHA.2013.v15.n2.a19
Classification : 16E30, 18E10, 19D99, 55U35
Keywords: Waldhausen category, abelian category, stable representation theory, homotopy colimit 
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     author = {Andrew Salch},
     title = {Homotopy colimits in stable representation theory},
     journal = {Homology, homotopy, and applications},
     pages = {331--360},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a19/}
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Andrew Salch. Homotopy colimits in stable representation theory. Homology, homotopy, and applications, Tome 15 (2013) no. 2, pp. 331-360. doi : 10.4310/HHA.2013.v15.n2.a19. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n2.a19/

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