[Alta-Logic] Peripatetic talk: Wed. 2nd Nov.

[Robin Cockett]

Time:  11:00am, November 2nd,  2011

Place: ICT616

Speaker: Kristine Bauer

Title: Homotopy (co)limits, II

The homotopy colimit (or limit) of a diagram is the universal object 
which completes a diagram into one which has a terminal (initial) 
object.  Heuristically, it can be thought of as assembling the 
information in a diagram into some kind of union.  In homotopy theory, 
where one only wants to work with equivalence classes of objects up to 
weak equivalence, the homotopy (co)limit can be problematic as it does 
not preserve the equivalence relation.  Last week, Tristan Jugdev 
explained the problems with  (co)limits, the idea of a homotopy 
(co)limit, and the constructions used by topologists to compute homotopy 
(co)limits.  In this talk, I will explain the homotopy (co)limit as a 
derived functor of the (co)limit.  I will explain to what extent a 
homotopy (co)limit does or does not satisfy a universal property.  I 
will explain how non-topological categories which have a well defined 
equivalence relation, such as the category of chain complexes, also have 
homotopy (co)limit constructions.  We'll explore some examples of these.