preprint

[Marco Grandis <grandis@dima.unige.it>]

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The following preprint is available:

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E. Carletti - M. Grandis
Fundamental groupoids as generalised pushouts of codiscrete groupoids
Dip. Mat. Univ. Genova, Preprint 603 (2013).
 	http://www.dima.unige.it/~grandis/GpdClm.pdf

Abstract. Every differentiable manifold X has a ‘good cover’, where  
all open sets and their finite intersections are contractible. Using  
a generalised van Kampen theorem for open covers we deduce that the  
fundamental groupoid of X is a ‘generalised pushout’ of codiscrete  
groupoids and inclusions.
This fact motivates the present brief study of generalised pushouts.  
In particular, we show that every groupoid is up to equivalence a  
generalised pushout of codiscrete subgroupoids, and that (in any  
category) finite generalised pushouts amount to ordinary pushouts and  
coequalisers.
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Before submitting it, I would like to know if the ‘generalised  
pushouts’ we are using (or similar colimits) have been considered  
elsewhere.
(They are not simply connected colimits, in the sense of Bob Pare,  
and indeed they cannot be constructed with pushouts.)

With best regards to all colleagues and friends. In particular to  
Ronnie Brown and Bob Pare, whose results are used in this preprint.

Marco

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