## Presentations of Omega-Categories By Directed Complexes (1997)

Citations: | 2 - 2 self |

### BibTeX

@MISC{Crans97presentationsof,

author = {Sjoerd E. Crans and Richard Steiner},

title = {Presentations of Omega-Categories By Directed Complexes},

year = {1997}

}

### OpenURL

### Abstract

The theory of directed complexes is extended from free !-categories to arbitrary !- categories by defining presentations in which the generators are atoms and the relations are equations between molecules. Our main result relates these presentations to the more standard algebraic presentations; we also show that every !-category has a presentation by directed complexes. The approach is similar to that used by Crans for pasting presentations. 1991 Mathematics Subject Classification: 18D05. 1 Introduction There are at present three combinatorial structures for constructing !-categories: pasting schemes, defined in 1988 by Johnson [8], parity complexes, introduced in 1991 by Street [16, 17] and directed complexes, given by Steiner in 1993 [15]. These structures each consist of cells which have collections of lower dimensional cells as domain and codomain; see for example Definition 2.2 below. They also have `local' conditions on the cells, ensuring that a cell together with its boundin...