Abstract

The main motivation of the paper lies in an argument which shows the relevance of the topological notion of lifting for semantic theory. After a brief examination of aspects of knowledge which are described by means of concepts of algebraic geometry, the development of a functorial connection between topology and group theory is related to aspects of logical analysis. In categorical terms, lifting is, with extension, a form of division. As such it is investigated here, starting from simple examples in general topology up to fiber spaces and topoi, in order to appreciate the recurrent pattern, which is finally used to explain the understanding of sentences about abstract domains.