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Macquarie University  Department of Mathematics

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Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Thu, 14 July:  14:00 - 15:00

Batanin weak higher groupoids and homotopy types
Cisinski, Denis-Charles (Université Paris 13)

The operadic approach of M.\ Batanin and R.\ Street to higher category theory in terms of trees allows us to define in a precise way the notion of weak higher category and of weak higher groupoid (higher category in which the $n$-arrows are invertible up to higher homotopies).

Moreover, Batanin constructed a functor from topological spaces to higher groupoids and conjectured that with a suitable notion of weak equivalences between weak higher groupoids, this should define an equivalence of categories between the homotopy category of CW-complexes and the homotopy category of weak higher groupoids.

Using constructions and results of C.\ Berger on the homotopy theory of (variants of) Joyal cellular sets, it is possible to show a first result in that direction: the homotopy type of any topological space can be reconstructed from its associated weak higher groupoid.

Typeset PDF of this abstract.