Dr. Moritz Groth, Universität Bonn, Vortrag: Grothendieck derivators: taking (derived) limits serious
Thursday, 24.11.2016 16:30 im Raum M5
Abstract: Category theory is a convenient unifying language which puts
into practice the following slogan. 'In order to study mathematical
objects one should also consider suitable morphisms between them.' For
instance, the basic language of category theory allows us to realize that
seemingly different constructions arising in various fields of mathematics
are instances of the same abstract notion (such as limit and colimit
While being a very useful language, category theory also has its
limitations. For instance in algebra and algebraic geometry one often
wants to identify quasi-isomorphic chain complexes while in homotopy
theory one does not want to distinguish weakly homotopy equivalent spaces.
The study of such identifications and compatible constructions lies beyond
the scope of category theory and it instead asks for more refined tools.
During roughly the last sixty years, various alternative such tools have
been proposed, and they constitute the huge field of Homotopical Algebra
or Higher Category Theory. In this talk, we will give a short introduction
to one such approach, namely the theory of derivators. Going back to
Anderson, Franke, Grothendieck, Heller, and others (in the alphabetic
order!), this approach emphasizes the calculus of derived limits and
colimits. By taking a representation theoretic perspective, we also intend
to shed additional light on more classical approaches.