Directed Algebraic Topology,Categories and Higher Categories |
| |
Authors: | Marco Grandis |
| |
Institution: | (1) Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy |
| |
Abstract: | Directed Algebraic Topology is a recent field, deeply linked with Category Theory. A ‘directed space’ has directed homotopies
(generally non reversible), directed homology groups (enriched with a preorder) and fundamental n-categories (replacing the fundamental n-groupoids of the classical case). On the other hand, directed homotopy can give geometric models for lax higher categories.
Applications have been mostly developed in the theory of concurrency. Unexpected links with noncommutative geometry and the
modelling of biological systems have emerged.
Work partially supported by MIUR Research Projects. |
| |
Keywords: | Directed algebraic topology Homotopy theory 2-categories Lax categories Fundamental n-category Concurrent processes |
本文献已被 SpringerLink 等数据库收录! |
|