7 Feb 2006

Susan Niefield

Homotopy Slices of Top and Exponentiability

Given a fixed topological space B, we consider exponentiablility in
the homotopy slice Top//B, i.e., the bicategory whose 0-cells are
continuous maps p:X-->B, 1-cells are triangles which commute up to a
specified homotopy, and 2-cells are equivalence classes of certain
homotopies between them.  After describing a right adjoint to the
inclusion in Top//B of the strict 2-slice Top/B, we present a class of
maps over B for which the homotopy pullback functor on Top/B has a
right biadjoint, and show how to extend this biadjoint to all of
Top//B.