EVENT DETAILS AND ABSTRACT

Title: Lifting properties and the small object argument
Speaker: Emily Riehl
Speaker Info: Harvard University
Brief Description:
Special Note:
Abstract:

Many constructions in homotopy theory rely on a good supply of maps satisfying lifting or extension properties, as axiomatized in Quillen's model categories. We describe a modified version of the small object argument, due to Richard Garner, for which the factorizations providing the good supply of maps bear a much closer relationship to the designated lifting properties. The functors produced in this manner allow for tighter "algebraic" control over constructions involving (trivial) fibrations or cofibrations, and fibrant or cofibrant objects. The construction we describe is available quite generally; hence its implications for ordinary and enriched model categories should have wide interest.