Cohomology enhanced: an application of enriched and higher categories

点击翻译按钮获取中文摘要

Motivated by the needs of physicists, computer scientists, and colleagues in other similar fields, mathematicians study highly complicated structures which are typically hard to understand completely in concrete terms. Cohomology is an invaluable technical tool which allows data to be extracted from these complex structures. This project will involve a radical expansion in scope of the amount and type of data so extracted. This is made possible by the most recent advances in higher-dimensional category theory.