Spans of cospans in a topos
| Autor: | Cicala, Daniel, Courser, Kenny |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Theory and Applications of Categories, Vol. 33, 2018, No. 1, pp 1-22 |
| Druh dokumentu: | Working Paper |
| Popis: | For a topos $\mathbf{T}$, there is a bicategory $\mathbf{MonicSp(Csp(T))}$ whose objects are those of $\mathbf{T}$, morphisms are cospans in $\mathbf{T}$, and 2-morphisms are isomorphism classes of monic spans of cospans in $\mathbf{T}$. Using a result of Shulman, we prove that $\mathbf{MonicSp(Csp(T))}$ 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 $\mathbf{MonicSp(Csp(Graph))}$. Comment: 22 pages |
| Databáze: | arXiv |
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