Abstract:
Given a fibration 
and a class 
of
arrows of 
, one can construct the free fibration (on 
over
such that all reindexing functors over elements of are
equivalences. In this work I give an explicit construction of this, and study
its properties. For example, the construction preserves the property of being
fibrewise discrete, and it commutes up to equivalence with fibrewise exact
completions. I show that mathematically interesting situations are examples
of this construction. In particular, subtoposes of the effective topos are
treated.
Available as PostScript, PDF, DVI.