Homotopy invariants of multiple categories and concurrency in computer science
نویسنده
چکیده
We associate to any (strict) multiple category C three homology theories : the rst one is called the globular homology and it contains the oriented loops of C ; both other ones are called corner homology, the negative one and the positive one, which contain the corners included in C. We make explicit the link between these homology theories and the homotopy of paths in multiple category. We construct two natural linear maps called the negative (resp. the positive) Hurewicz morphism from the globular homology to the negative (resp. positive) corner homology. At the end of the paper, we explain the reason why these theories are interesting for some geometric problems coming from computer science. Contents 1 Introduction 2 2 Cubical complex, multiple category and pasting scheme 3 2.1 Cubical complex and multiple category 3 2.2 Pasting scheme 4 2.3 The pasting scheme of the n-cube 6 2.4 Path functor and cubical nerve of a multiple category 7 3 Homotopy and multiple category 8 4 Globular homology of multiple category 11 4.1 Deenition 11 4.2 Projective globular group 12 4.3 Globular homology and homotopy of paths 13 5 Positive and negative corner homology of multiple category 14 5.1 Deenition 14 5.2 Combinatorial structure on the cubical nerve of a multiple category 15 5.3 Corner homology and homotopy of paths 23
منابع مشابه
4 M ar 1 99 9 Homotopy invariants of multiple categories and concurrency in computer science
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تاریخ انتشار 1999