{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T04:41:51Z","timestamp":1777956111977,"version":"3.51.4"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T00:00:00Z","timestamp":1764201600000},"content-version":"unspecified","delay-in-days":330,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2025]]},"abstract":"Abstract<\/jats:title>\n \n In this paper, we show that if\n \n \n \n $\\mathscr{C}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a category and if\n \n \n \n $F\\colon \\mathscr{C}^{\\;\\textrm {op}} \\to \\mathfrak{Cat}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a pseudofunctor such that for each object\n \n \n \n $X$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of\n \n \n \n $\\mathscr{C}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n the category\n \n \n \n $F(X)$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is a tangent category and for each morphism\n \n \n \n $f$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of\n \n \n \n $\\mathscr{C}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n the functor\n \n \n \n $F(\\,f)$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is part of a strong tangent morphism\n \n \n \n $(F(\\,f),\\!\\,_{f}{\\alpha })$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and that furthermore the natural transformations\n \n \n \n $\\!\\,_{f}{\\alpha }$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n vary pseudonaturally in\n \n \n \n $\\mathscr{C}^{\\;\\textrm {op}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , then there is a tangent structure on the pseudolimit\n \n \n \n $\\mathbf{PC}(F)$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n which is induced by the tangent structures on the categories\n \n \n \n $F(X)$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n together with how they vary through the functors\n \n \n \n $F(\\,f)$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . We use this observation to show that the forgetful\n \n \n \n $2$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -functor\n \n \n \n $\\operatorname {Forget}:\\mathfrak{Tan} \\to \\mathfrak{Cat}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n creates and preserves pseudolimits indexed by\n \n \n \n $1$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -categories. As an application, this allows us to describe how equivariant descent interacts with the tangent structures on the category of smooth (real) manifolds and on various categories of (algebraic) varieties over a field.\n <\/jats:p>","DOI":"10.1017\/s0960129525100273","type":"journal-article","created":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T06:02:50Z","timestamp":1764223370000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Pseudolimits for tangent categories with applications to equivariant algebraic and differential geometry"],"prefix":"10.1017","volume":"35","author":[{"given":"Dorette","family":"Pronk","sequence":"first","affiliation":[{"name":"Dalhousie University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5872-8326","authenticated-orcid":false,"given":"Geoff","family":"Vooys","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01e6qks80","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,11,27]]},"reference":[{"key":"S0960129525100273_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02950-3"},{"key":"S0960129525100273_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02699291"},{"key":"S0960129525100273_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-1524-5_4"},{"key":"S0960129525100273_ref17","first-page":"286","article-title":"Classifying tangent structures using weil algebras","volume":"9","author":"Leung","year":"2017","journal-title":"Theory Appl. Categ."},{"key":"S0960129525100273_ref20","volume-title":"Geometric Invariant Theory, Volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]","author":"Mumford","year":"1982"},{"key":"S0960129525100273_ref12","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198871378.001.0001"},{"key":"S0960129525100273_ref23","unstructured":"Vooys, G. (2021). Equivariant functors and sheaves. PhD. thesis. Available at https:\/\/arxiv.org\/abs\/2110.01130."},{"key":"S0960129525100273_ref5","volume-title":"\u00c9tale Cohomology and the Weil Conjecture, Volume 13 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]","author":"Freitag","year":"1988"},{"key":"S0960129525100273_ref21","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X22007783"},{"key":"S0960129525100273_ref7","volume-title":"Cohomologie Non Ab\u00e9lienne. Die Grundlehren Der Mathematischen Wissenschaften, Band 179","author":"Giraud","year":"1971"},{"key":"S0960129525100273_ref15","unstructured":"Lanfranchi, M. (2023). The Grothendieck construction in the context of tangent categories. Available at https:\/\/arxiv.org\/ abs\/2311.14643."},{"key":"S0960129525100273_ref4","first-page":"1077","article-title":"Differential bundles in commutative algebra and algebraic geometry","volume":"36","author":"Cruttwell","year":"2023","journal-title":"Theory Appl. Categ."},{"key":"S0960129525100273_ref24","unstructured":"Vooys, G. (2022). Equivariant tangent categories on varieties. Presentation at foundational methods in Computer Science 2022, Barrier Lake Field Station, Alberta, Canada. Slides available at https:\/\/pages.cpsc.ucalgary.ca\/\u223crobin\/FMCS\/FMCS2022\/slides\/GeoffVooyos.pdf."},{"key":"S0960129525100273_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10485-013-9312-0"},{"key":"S0960129525100273_ref1","volume-title":"Equivariant Sheaves and Functors, Volume 1578 of Lecture Notes in Mathematics","author":"Bernstein","year":"1994"},{"key":"S0960129525100273_ref3","unstructured":"Cruttwell, G. S. H. and Lanfranchi, M. 2025). Pullbacks in tangent categories and tangent display maps. arXiv preprint available at https:\/\/arxiv.org\/abs\/2502.20699."},{"key":"S0960129525100273_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2017.10.039"},{"key":"S0960129525100273_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02732123"},{"key":"S0960129525100273_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0058656"},{"key":"S0960129525100273_ref18","first-page":"217","volume-title":"Representations of groups (Banff, AB, 1994), volume 16 of CMS Conf. Proc.","author":"Lusztig","year":"1995"},{"key":"S0960129525100273_ref16","unstructured":"Lemay, J.-S. P. and Vooys, G. (2025). Horizontal descent, immersions, unramified morphisms, submersions, \u00e9tale morphisms and the relative cotangent sequence in tangent categories. Preprint available at, https:\/\/arxiv.org\/abs\/2506.07874."},{"key":"S0960129525100273_ref11","volume-title":"Algebraic Geometry, Volume 52 of Graduate Texts in Mathematics","author":"Hartshorne","year":"1977"},{"key":"S0960129525100273_ref19","unstructured":"MacAdam, B. (2022). The functorial semantics of Lie theory. PhD Thesis. Availabe at https:\/\/prism.ucalgary.ca\/items\/05830be5-fbdf-4be2-a9a5-cc1e73762d7f\/full."},{"key":"S0960129525100273_ref22","first-page":"JR1","article-title":"Abstract tangent functors","volume":"12","author":"Rosick\u00fd","year":"1984","journal-title":"Diagrammes"},{"key":"S0960129525100273_ref25","unstructured":"Vooys, G. (2024). Categories of pseudocones and equivariant descent. Preprint available at https:\/\/arxiv.org\/abs\/2401.10172."}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129525100273","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T01:07:54Z","timestamp":1777943274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129525100273\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":25,"alternative-id":["S0960129525100273"],"URL":"https:\/\/doi.org\/10.1017\/s0960129525100273","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}],"article-number":"e33"}}