Descent theory for lax algebras
by
Dirk Hofmann
University of Aveiro, Portugal
Coauthors: Maria Manuel Clementino (University of Coimbra, Portugal)

A common strategy in effective descent theory is to embed the category in question into a friendlier category and recognize there the effective descent maps using a ``pullback criterion'' (see [3] and [4]). In our study of categories Alg(T, e, m;V) of reflexive and transitive (T, V)-algebras (see [1] and [2]), the role of the larger category is played by the category Alg(T, e;V) of reflexive (T, V)-algebras, which is complete, cocomplete and-under certain circumstances-locally cartesian closed. Using this we are able to describe various classes of effective descent maps, having among them the classes of (suitably defined) open and proper surjections.

References

[1] M. M. Clementino and D. Hofmann, Topological features of lax algebras, Preprint 01-09, Department of Mathematics, University of Coimbra (2001) (http://www.mat.uc.pt/~categ/reports.html).

[2] M. M. Clementino and W. Tholen, Topology and Multicategory - a Common Approach, Preprint 01-10, Department of Mathematics, University of Coimbra (2001) (http://www.mat.uc.pt/~categ/reports.html).

[3] G. Janelidze and M. Sobral, Finite preorders and topological descent I, JPAA, to appear.

[4] J. Reiterman and W. Tholen, Effective descent maps of topological spaces, Top. Appl. 57 (1994), 53-69.

Date received: May 15, 2002