A recognition criterion for lax-idempotent pseudomonads

A recognition criterion for lax-idempotent pseudomonads | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A recognition criterion for lax-idempotent pseudomonads John Bourke This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8407365/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract We describe a simple criterion which makes it easy to recognise when a pseudomonad is lax-idempotent. The criterion concerns the behaviour of colax bilimits of arrows - certain comma objects - and is easy to verify in examples. Building on this, we obtain a new characterisation of lax-idempotent pseudomonads on 2-categories with colax bilimits of arrows. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Apr, 2026 Reviews received at journal 16 Apr, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers invited by journal 07 Jan, 2026 Editor assigned by journal 21 Dec, 2025 Submission checks completed at journal 21 Dec, 2025 First submitted to journal 19 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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