Seminarium z Topologii Algebraicznej
Wtorki, 12:15-13:45, sala 4070
17.XII.2013
Karol Szumiło (Bonn University)
Cofibration categories and quasicategories
Classically, homotopy theories are described using homotopical algebra,
e.g. as model categories or (co)fibration categories. Nowadays, they are
often formalized as higher categories, e.g. as quasicategories or complete
Segal spaces. These two types of approaches highlight different aspects of
abstract homotopy theory and are useful for different purposes. Thus it isan interesting question whether homotopical algebra and higher category
theory are in some precise sense equivalent.
In this talk I will concentrate on cofibration categories and
quasicategories. I will discuss some basic features of both notions
building up to a result that the homotopy theory of cofibration categories
is indeed equivalent to the homotopy theory of cocomplete quasicategories.