Tim Porter (University of Wales Bangor)
t.porter@bangor.ac.uk
Any equivalence relation can be regarded as a groupoid in an almost naive way. Any map between spaces leads to an equivalence relation on the domain and if the map is a fibration, that equivalence relation has a nice structure. That structure is inherited by the fundamental groupoid and leads to a crossed module structure. That much is almost classical.
Crossed modules are just the bottom of a range of higher dimensional algebraic structures that have been gradually gaining favour in topology and related areas of geometry. The talk will review the topological results on crossed modules and their higher dimensional analogues and how they relate to fibrations, fibrant squares and related gadgets and then will use similar methods with simplicial groups to derive model for higher n-types.