Spans of cospans. (English) Zbl 1412.18008
The author explains how to compose horizontally and vertically spans of cospans in a category \(\mathbf{C}\). The main theorem of this paper then states that in a topos \(\mathbf{C}\), and when the legs of the spans are monic, these two forms of composition satisfy the interchange law. In this case there is a bicategory of objects, cospans, and “monic-legged” spans of cospans in \(\mathbf{C}\). One motivation for this construction is an application to graph rewriting.
Reviewer: Philippe Gaucher (Paris)
MSC:
| 18D05 | Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) |
| 68Q42 | Grammars and rewriting systems |
| 90B10 | Deterministic network models in operations research |
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