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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 63, Issue 1
  • August 1997, pp. 47-77

Presentations of omega-categories by directed complexes

  • Sjoerd E. Crans (a1) and Richard Steiner (a2)
  • DOI: http://dx.doi.org/10.1017/S1446788700000318
  • Published online: 01 April 2009
Abstract
Abstract

The theory of directed complexes is extended from free ω-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 ω-category has a presentation by directed complexes. The approach is similar to that used by Crans for pasting presentations.

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[2]J. C. Baez and J. Dolan , ‘Higher dimensional algebra and topological quantum field theory’. J. Math. Phys. 36 (1995), 60736105.

[8]M. Johnson , ‘The combinatorics of n-categorical pasting’, J. Pure Appl. Algebra 62 (1989), 211225.

[10]M. M. Kapranov and V. A. Voevodsky , ‘Braided monoidal 2-categories, 2-vector spaces and Zamolodchikov's tetrahedra equations’, J. Pure Appl. Algebra 92 (1994), 241267.

[15]R. Steiner , ‘The algebra of directed complexes’, Appl. Categorical Structures 1 (1993), 247284.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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