Modelling fundamental 2-categories for directed homotopy (*)
نویسنده
چکیده
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 (generally non reversible) and fundamental n-categories (replacing the fundamental ngroupoids of the classical case). Finding a simple model of the latter is a non-trivial 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 wider than categorical equivalence. Taking on a previous work on "The shape of a category up to directed homotopy", we study now the fundamental 2category of a directed space. All the notions of 2-category theory used here are explicitly reviewed.
منابع مشابه
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. Applicatio...
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