9 November 2004 
2:30 - 4:00   J Funk

Purely Skeletal Geometric Morphisms (II)
Joint with Marta Bunge

Abstract: We continue our investigation of geometric morphisms whose
inverse image functor preserves pure monomorphisms, where a monomorphism
in a topos is said to be pure if the constant object 2 has the sheaf
property with respect to every pullback of the monomorphism.
(For instance, the complement of a knot is a pure open subset of S^3.)
One of our goals is to improve our understanding of branched coverings,
which we define as a subclass of the class of complete spreads.  We
say that a complete spread is a branched covering if it is i) purely
skeletal, and ii) locally constant, but we allow the splitting object to
have only pure, instead of global, support.  The smallest pure
subtopos (of sheaves for pure monomorphisms) plays an interesting role in
these investigations.  For instance, the category of locally constant
coverings of a pure subobject of 1 embeds into the category of locally
constant coverings of the smallest pure subtopos.