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A coalgebraic model of graphs

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arxiv 1508.02169 v3 pith:QDCUDSIG submitted 2015-08-10 math.CO math.CT

Christian Jäkel This is my paper · ORCID
classification math.COmath.CT
keywords graphsmodelcategorycoalgebrasarbitrarycategoriescoalgebracoalgebraic
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abstract

For a set-endofunctor $F$, a graph is triple $(V,E,g)$ with a structure map $g:E\rightarrow F V$. This model is a generalized coalgebra over the category of sets. In this note, we model graphs as coalgebras over $Set\times Set$ and use the theory of coalgebras over arbitrary categories to conclude properties of the category of graphs.

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  1. Cellular sheaf Laplacians on the set of simplices of symmetric simplicial set induced by hypergraph

    math.AT 2024-11 conditional novelty 6.0 of 10

    Cellular sheaf Laplacians are generalized to symmetric simplicial sets induced by hypergraphs, with a Hodge theorem connecting their kernels to sheaf cohomology.

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