CLASSIFYING-SPACES, CLASSIFYING TOPOI AND AUGMENTED ORDERS

It is shown that the classifying space of a topological category has t he same weak homotopy type as the classifying topos. As a consequence, mappings from a CW-complex X into the classifying topos. As a consequ ence, mappings from a CW-complex X into the classifying space are show n lo correspond to concordance classes of augmented orders over X.