Homology, Homotopy and Applications
Volume 8 (2006)
Modelling fundamental 2-categories for directed homotopy
Pages: 31 – 70
Directed Algebraic Topology is a recent field, deeply linked with ordinary and higher dimensional Category Theory. A ‘directed space’, e.g. an ordered topological space, has directed homotopies (which are generally non-reversible) and fundamental n-categories (replacing the fundamental $n$-groupoids of the classical case). Finding a simple model of the latter is a nontrivial problem, whose solution gives relevant information on the given ‘space’; a problem which is also of interest in general Category Theory, as it requires equivalence relations which are more general than categorical equivalence. Taking on a previous work on ‘The shape of a category up to directed homotopy’, we study now the fundamental 2-category of a directed space. All the notions of 2-category theory used here are explicitly reviewed.
2-functors, local adjunctions, homotopy theory, directed algebraic topology, fundamental 2-category
2010 Mathematics Subject Classification
18A40, 18D05, 55Pxx, 55Qxx, 55Uxx