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A simplicial description of the homotopy category of simplicial groupoids

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A. R. Garzon, J. G. Miranda and R. Osorio

In this paper we use Quillen's model structure given by Dwyer-Kan for the
category of simplicial groupoids (with discrete object of objects) to
describe in this category, in the simplicial language, the fundamental
homotopy theoretical constructions of path and cylinder objects. We then
characterize the associated left and right homotopy relations in terms of
simplicial identities and give a simplicial description of the homotopy
category of simplicial groupoids. Finally, we show loop and suspension
functors in the pointed case.

Keywords: closed model category, path object, cylinder object, homotopy relation.

2000 MSC: 18G30, 55U35.

Theory and Applications of Categories, Vol. 7, 2000, No. 14, pp 263-283.

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