Geodesic
Spans of cospans in a topos
Theory and applications of categories, Tome 33 (2018), pp. 1-22

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For a topos T, there is a bicategory MonicSp(Csp(T)) whose objects are those of T, morphisms are cospans in T, and 2-morphisms are isomorphism classes of monic spans of cospans in T. Using a result of Shulman, we prove that MonicSp(Csp(T)) is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as 2-morphisms inside a compact closed sub-bicategory of MonicSp(Csp(Graph)).

Publié le :
Classification : 16B50, 18D05 and 18D10
Keywords: bicategory, graph rewrite, network, span, symmetric monoidal, topos 
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     author = {Daniel Cicala and Kenny Courser},
     title = {Spans of cospans in a topos},
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     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a0/}
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Daniel Cicala; Kenny Courser. Spans of cospans in a topos. Theory and applications of categories, Tome 33 (2018), pp. 1-22. http://geodesic.mathdoc.fr/item/TAC_2018_33_a0/