Wojciech Chacholski (Stockholm)


Representations of spaces and mapping complexes

ABSTRACT:
derived functors of colimits and limits, mapping complexes, fibrant 
and cofibrant replacements are fundamental objects of homotopy 
theory. The frameworks which have been developed in order to study 
these constructions range  from model categories to theory of 
derivators.   These approaches however are not easy to use. For
example it is often a difficult task to impose a model structure 
that reflects desired properties. Even if one is able to prove its 
existence, such a statement shades little info on how to construct
cofibrant/ fibrant replacements. In the talk I will explain a modified
approach, the key feature of which is its simplicity and applicability.
This is joint work with J. Scherer.