Inessential directed maps and directed homotopy equivalences
نویسندگان
چکیده
منابع مشابه
On directed homotopy equivalences and a notion of directed topological complexity
This short note introduces a notion of directed homotopy equivalence (or dihomotopy equivalent) and of “directed” topological complexity (which elaborates on the notion that can be found in e.g. [9]) which have a number of desirable joint properties. In particular, being dihomotopically equivalent implies having bisimilar natural homologies (defined in [5]). Also, under mild conditions, directe...
متن کاملThe Directed Homotopy Hypothesis
The homotopy hypothesis was originally stated by Grothendieck [13] : topological spaces should be “equivalent” to (weak) ∞-groupoids, which give algebraic representatives of homotopy types. Much later, several authors developed geometrizations of computational models, e.g. for rewriting, distributed systems, (homotopy) type theory etc. But an essential feature in the work set up in concurrency ...
متن کاملDirected Homotopy Theory
Résumé. La Topologie Algébrique Dirigée est en train d'émerger, à partir de plusieurs applications. La structure de base que nous étudions ici, un espace dirigé ou d-éspace, est un éspace topologique muni d'une famille convenable de chemins dirigés. Dans ce cadre, les homotopies dirigées, généralement non réversibles, sont répresentées par des foncteurs cylindre et cocylindre. L'existence des r...
متن کاملDirected Homotopy Theory , I
Résumé. La Topologie Algébrique Dirigée est en train d'émerger, à partir de plusieurs applications. La structure de base que nous étudions ici, un espace dirigé ou d-éspace, est un éspace topologique muni d'une famille convenable de chemins dirigés. Dans ce cadre, les homotopies dirigées, généralement non réversibles, sont répresentées par des foncteurs cylindre et cocylindre. L'existence des r...
متن کاملModelling fundamental 2-categories for directed homotopy (*)
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 r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 2020
ISSN: 0308-2105,1473-7124
DOI: 10.1017/prm.2020.64