Spined categories: generalizing tree-width beyond graphs

04/05/2021

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by   Benjamin Merlin Bumpus, et al.

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We develop a general theory of categories that admit a functorial invariant (the triangulation functor) which generalizes the tree-width of graphs. Our triangulation functor provides a uniform construction for various tree-width-like invariants including hypergraph tree-width, and the tree-width of the modular quotient in the category of modular partition functions.