{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/morphisms-of-neural-codes","title":"Morphisms of Neural Codes","arxiv_id":"1806.02014","date":"2018-06-06","proceeding":null,"authors":["R. Amzi Jeffs"],"abstract":"We define a notion of morphism between combinatorial codes, making the class of all combinatorial codes into a category $\\mathbf{Code}$. We show that morphisms can be used to remove redundant information from a code, and that morphisms preserve convexity. This fact leads us to define \"minimally non-convex\" codes. We propose a program to characterize these minimal obstructions to convexity and hence characterize all convex codes. We implement a library of Sage code to perform computation with morphisms. These computational methods yield the smallest to-date example of a non-convex code with no local obstructions. We conclude by giving an algebraic formulation of our results.","url_abs":"https://arxiv.org/abs/1806.02014v3","url_pdf":"https://arxiv.org/pdf/1806.02014v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"morphisms-of-neural-codes","repo_url":"https://github.com/AmziJeffs/Neural-Code-Morphisms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1806.02014","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}