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Monoidal Width: Unifying Tree Width, Path Width and Branch Width
- Publication Year :
- 2022
-
Abstract
- We introduce monoidal width as a measure of the difficulty of decomposing morphisms in monoidal categories. For graphs, we show that monoidal width and two variations capture existing notions, namely branch width, tree width and path width. We propose that monoidal width: (i) is a promising concept that, while capturing known measures, can similarly be instantiated in other settings, avoiding the need for ad-hoc domain-specific definitions and (ii) comes with a general, formal algebraic notion of decomposition using the language of monoidal categories.<br />Comment: 28 pages
- Subjects :
- Mathematics - Category Theory
Computer Science - Logic in Computer Science
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2202.07582
- Document Type :
- Working Paper