#
Thin elements and commutative shells in cubical omega-categories

##
Philip J. Higgins

The relationships between thin elements,
commutative shells and connections in cubical omega-categories are
explored by a method which does not involve the use of pasting
theory or nerves of omega-categories (both of which were previously
needed for this purpose; see Al-Agl, Brown and Steiner, Section 9). It is
shown that composites of commutative shells are commutative and
that thin structures are equivalent to appropriate sets of
connections; this work extends to all dimensions the results
proved in dimensions 2 and 3 in Brown, Kamps and Porter and Brown and
Mosa.

Keywords:
cubical omega-category, connections, thin
elements, thin structure, folding operations, commutative shells

2000 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 14, 2005,
No. 4, pp 60-74.

http://www.tac.mta.ca/tac/volumes/14/4/14-04.dvi

http://www.tac.mta.ca/tac/volumes/14/4/14-04.ps

http://www.tac.mta.ca/tac/volumes/14/4/14-04.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/4/14-04.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/4/14-04.ps

TAC Home