On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps

Abstract

A previous paper constructed exponential laws in the category Top_B of spaces over B. The present paper relates these laws to constructions known for locally trivial maps, and constructs also new exponential laws for ex-spaces, fibred section spaces and fibred relative lifting spaces. Versions of these laws for homotopy classes of maps are discussed.