Directed Algebraic Topology, Categories and Higher Categories

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 ngroupoids 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.

• Type: Journal
• Year: 2007
• Where: ACS
• Authors: Marco Grandis
• Keywords: ACS 2007, Category Theory, Directed Algebraic Topology, Distributed And Parallel Computing, Homology Groups