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The coalgebraic structure of cell complexes

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Thomas Athorne

The relative cell complexes with respect to a generating set of
cofibrations are an important class of morphisms in any model structure.
In the particular case of the standard (algebraic) model structure on
**Top**, we give a new expression of these morphisms by defining a
category of relative cell complexes, which has a forgetful functor to the
arrow category. This allows us to prove a conjecture of Richard Garner:
considering the algebraic weak factorisation system given in that
algebraic model structure between cofibrations and trivial fibrations, we
show that the category of relative cell complexes is equivalent to the
category of coalgebras.

Keywords:
relative cell complexes, algebraic weak factorisation systems, small
object argument

2000 MSC:
18A32, 55U35

*Theory and Applications of Categories,*
Vol. 26, 2012,
No. 11, pp 304-330.

Published 2012-06-13.

http://www.tac.mta.ca/tac/volumes/26/11/26-11.dvi

http://www.tac.mta.ca/tac/volumes/26/11/26-11.ps

http://www.tac.mta.ca/tac/volumes/26/11/26-11.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/11/26-11.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/26/11/26-.11ps

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