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Earlier trustworthiness-based proposals define synchronic and diachronic identity using trustworthiness levels, but leave implicit the structure of compared states and the transformations that connect them. A category-theoretic framework formalizes AI identity with lifecycle paths, admissible functors, and natural transformations.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/a-category-theory-account-of-ai-identity/327129/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/a-category-theory-account-of-ai-identity/327129.png","ImageObject",300,407,{"name":92,"@type":93},"Logic","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-08","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why does AI governance depend on metaphysical questions about identity?","Question",{"text":112,"@type":113},"Because evaluations, fairness analyses, and monitoring results are produced for a particular system under particular conditions, and applying them to later versions or deployments presupposes sufficient identity. Regulatory notions like “substantial modification” also distinguish changes that preserve the governed object from those that generate a new one.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the earlier trustworthiness-based approach define AI identity?",{"text":117,"@type":113},"It formulates synchronic and diachronic identity propositionally by relating identity within a fixed AI system type to equality of trustworthiness levels. This specifies when identity statements are true, but does not make the compared state structure or transformation structure explicit.",{"name":119,"@type":110,"acceptedAnswer":120},"What does the category-theoretic account add to these propositional criteria?",{"text":121,"@type":113},"It models AI system types using a structured datum that includes trustworthiness information, connects profile-relative states by admissible lifecycle paths restricted to trustworthiness-level-preserving transformations, and represents histories with temporally admissible functors. The approach yields weak and strong categorical interpretations of the earlier criteria, replacing a single identity relation with a hierarchy of diachronic and synchronic conditions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},327129,1790374656,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","arXiv :2607 .00220v1 [math .CT] 30 Jun 2026  \nA CATEGORY THEORY ACCOUNT OF AI IDENTITY  \nAndrea Ferrario 1,2,3  \n1 Institute of Biomedical Ethics and History of Medicine, University of Zürich, Zürich, Switzerland  \n2 SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA), Lugano, Switzerland  \n3 ETH Zürich, Zürich, Switzerland  \nJuly 2, 2026  \nABSTRACT  \nArtificial intelligence (AI) systems are routinely modified after deployment through retraining, reconfiguration, and changes in their operational environments. These transformations raise a metaphysical question with direct consequences for AI governance: under what conditions does an AI system remain the same system over time or across deployments? Earlier trustworthiness-based work formulates synchronic and diachronic identity propositionally, by relating identity within a fixed AI system type to equality of trustworthiness levels. Such criteria specify when identity statements are true, but leave implicit the structure of the states compared, the transformations connecting them, and the temporal organization of persistence.  \nWe develop a category-theoretic formalization of AI identity. An AI system type is specified by a datum ♢ = (F, P, LP ), consisting of a techno-function, a trustworthiness profile, and a trustworthiness-level function. Profile-relative states are connected by admissible lifecycle paths, which are restricted to trustworthiness-level-preserving transformations and quotiented to obtain a thin reachability category. Temporally admissible functors represent AI system histories, while time-synchronous natural transformations compare realized histories.  \nThe formalization yields two categorical interpretations of the earlier propositional criteria. A weak interpretation recovers identity, within a fixed datum ♢, as equality of trustworthiness level. A strong interpretation refines it by requiring mutual trustworthiness-preserving reachability, expressed through state isomorphism or natural isomorphism of realized histories. Category theory therefore replaces a single undifferentiated identity relation with a structured hierarchy of diachronic and synchronic criteria. The resulting framework identifies identity-related preconditions for transferring responsible-AI claims, evidence, and governance procedures across versions or deployments, without treating categorical identity as sufficient by itself for such transfer.  \nKeywords: AI identity; artificial intelligence systems; trustworthiness; category theory; artifact metaphysics; AI governance; lifecycle management; MLOps.  \n1 Introduction  \nThe idea that entities require identity criteria for ontological respectability has a long philosophical tradition, canonically expressed by Quine’s dictum “no entity without identity” [Quine, 1969, p. 44] . Identity criteria specify the conditions under which an entity at one time or in one setting is the same as, or different from, an entity at another. Without such criteria, it remains unclear what is being counted, compared, governed, or held responsible across change.  \nArtificial intelligence (AI) systems make this longstanding problem especially pressing. Deployed AI systems are routinely modified through retraining, fine-tuning, recalibration, threshold adjustment, model replacement, rollback, data refresh, pipeline reconfiguration, monitoring interventions, and changes in their operational environments [Kreuzberger et al., 2023] . These transformations may be necessary to correct errors, respond to distribution shift, improve fairness or robustness, adapt a system to changing operational or responsible-AI requirements. Some systems are accessed globally through large numbers of personalized or deployment-specific instances. These changes and apparent multiplicity  \nraise the metaphysical question: when does a changing AI system remain the same system? And, further, when are AI systems the same system? These classical metaphysical questions have immedia","cbCail5D9BhcdUwz","https://ap.wps.com/l/cbCail5D9BhcdUwz","pdf",610450,25,"English","# Abstract\n# 1 Introduction\n## Identity criteria and ontological respectability\n## Governance consequences of AI modification\n## Prior work on AI identity and trustworthiness","[{\"question\":\"Why does AI governance depend on metaphysical questions about identity?\",\"answer\":\"Because evaluations, fairness analyses, and monitoring results are produced for a particular system under particular conditions, and applying them to later versions or deployments presupposes sufficient identity. Regulatory notions like “substantial modification” also distinguish changes that preserve the governed object from those that generate a new one.\"},{\"question\":\"How does the earlier trustworthiness-based approach define AI identity?\",\"answer\":\"It formulates synchronic and diachronic identity propositionally by relating identity within a fixed AI system type to equality of trustworthiness levels. This specifies when identity statements are true, but does not make the compared state structure or transformation structure explicit.\"},{\"question\":\"What does the category-theoretic account add to these propositional criteria?\",\"answer\":\"It models AI system types using a structured datum that includes trustworthiness information, connects profile-relative states by admissible lifecycle paths restricted to trustworthiness-level-preserving transformations, and represents histories with temporally admissible functors. The approach yields weak and strong categorical interpretations of the earlier criteria, replacing a single identity relation with a hierarchy of diachronic and synchronic conditions.\"}]","A CATEGORY THEORY ACCOUNT OF AI IDENTITY | PDF",1789976493,63]