Toposes are adhesive

Authors:
Stephen Lack;Paweł Sobociński
Affiliations:
School of Computing and Mathematics, University of Western Sydney, Australia;Computer Laboratory, University of Cambridge, United Kingdom
Venue:
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Year:
2006

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Abstract

Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.