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Categorical models and quasigroup homotopies

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George Voutsadakis

In many applications of quasigroups
isotopies and homotopies are more important than isomorphisms and homomorphisms.
In this paper, the way homotopies may arise in the context of
categorical quasigroup model theory is investigated. In this context, the
algebraic structures are specified by diagram-based logics, such as sketches, and categories
of models become functor categories.
An idea, pioneered by Gvaramiya and Plotkin, is used to give a construction of
a model category naturally equivalent to the category of quasigroups with
homotopies between them.

Keywords: sketches, finite product sketches, sketch models, quasigroups, homotopies.

2000 MSC: 20N05, 18B99, 18A10

*Theory and Applications of Categories*, Vol. 11, 2003,
No. 1, pp 1-14.

http://www.tac.mta.ca/tac/volumes/11/1/11-01.dvi

http://www.tac.mta.ca/tac/volumes/11/1/11-01.ps

http://www.tac.mta.ca/tac/volumes/11/1/11-01.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/1/11-01.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/1/11-01.ps

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