Simplification for Graph-like Objects

2020/12/16 by Will Grilliette, Grilliette, Will
Computer Science · #05C20 #05C65 #18A25 #18A40 #Advanced Algebra and Logic #Category Theory (math.CT) #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2012.08772

openalex publication_date 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the functor-structured category. Seated in categorical terms, simplification can be dualized to "antisimplification", which manifests as removal of isolated vertices and loose edges.

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