Homotopy invariants of higher dimensional categories and concurrency in computer science

Homotopy invariants of higher dimensional categories and concurrency in computer science

The strict globular ω-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) ω-category C three homology theories. The first one is called the globular homology. It contains the oriented loops of C. The two other ones are called the negative (resp. positive ) corner homology. They contain in a certain manner the branchi...

Homotopy invariants of multiple categories and concurrency in computer science

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 con...

4 M ar 1 99 9 Homotopy invariants of multiple categories and concurrency in computer science

Homotopy invariants and time evolution in (2+1)-dimensional gravity.

We establish the relation between the ISO(2, 1) homotopy invariants, and the polygon representation of (2+1)-dimensional gravity. The polygon closure conditions, together with the SO(2, 1) cycle conditions, are equivalent to the ISO(2, 1) cycle conditions for the representations ρ : π 1 (Σ g,N) → ISO(2, 1). Also, the symplectic structure on the space of invariants is closely related to that of ...

Some Aspects of Categories in Computer Science