Omegacategories and chain complexes
Abstract
There are several ways to construct omegacategories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we call augmented directed complexes. This functor from augmented directed complexes to omegacategories has a left adjoint, and the adjunction restricts to an equivalence on a category of augmented directed complexes with good bases. The omegacategories equivalent to augmented directed complexes with good bases include the omegacategories associated to globes, simplexes and cubes; thus the morphisms between these omegacategories are determined by morphisms between chain complexes. It follows that the entire theory of omegacategories can be expressed in terms of chain complexes; in particular we describe the biclosed monoidal structure on omegacategories and calculate some internal homomorphism objects.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403237
 Bibcode:
 2004math......3237S
 Keywords:

 Category Theory;
 18D05
 EPrint:
 18 pages