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Being Van Kampen is a universal property

Pawel Sobocinski ; Tobias Heindel.

Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are&nbsp;[&hellip;]

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Rule Algebras for Adhesive Categories

Nicolas Behr ; Pawel Sobocinski.

We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably, our results hold in the general setting of&nbsp;[&hellip;]

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Monoidal Width

Elena Di Lavore ; Paweł Sobociński.

We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition: a monoidal decomposition of a morphism is an&nbsp;[&hellip;]

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