{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T06:23:12Z","timestamp":1671085392708},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T00:00:00Z","timestamp":1667952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,12,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Generalizing slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann (2015, Higher-Order Computability), we define canonical strict computability models over certain categories and appropriate presheaves on them. We study the canonical total computability model over a category $\\mathcal {C}$ and a covariant presheaf on $\\mathcal {C}$ and the canonical partial computability model over a category $\\mathcal {C}$ with pullbacks and a pullback preserving, covariant presheaf on $\\mathcal {C}$. These strict computability models are shown to be special cases of a strict computability model over a category $\\mathcal {C}$ with a so-called base of computability and a pullback preserving, covariant presheaf on $\\mathcal {C}$, connecting in this way Rosolini\u2019s theory of dominions with the theory of computability models. All our notions and results are dualized by considering certain (contravariant) presheaves on appropriate categories.<\/jats:p>","DOI":"10.1093\/logcom\/exac077","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T13:28:24Z","timestamp":1664371704000},"page":"1815-1838","source":"Crossref","is-referenced-by-count":0,"title":["Strict computability models over categories and presheaves"],"prefix":"10.1093","volume":"32","author":[{"given":"Iosif","family":"Petrakis","sequence":"first","affiliation":[{"name":"Mathematics Institute , Ludwig-Maximilians Universit\u00e4t M\u00fcnchen, 80333 M\u00fcnchen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,11,9]]},"reference":[{"key":"2022121408225653800_ref1","volume-title":"Categories and Computability","author":"Cockett","year":"2014"},{"key":"2022121408225653800_ref2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.apal.2008.04.005","article-title":"Introduction to Turing categories","volume":"156","author":"Cockett","year":"2008","journal-title":"Annals of Pure and Applied Logic"},{"key":"2022121408225653800_ref3","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1016\/j.jpaa.2009.12.028","article-title":"Categorical simulations","volume":"214","author":"Cockett","year":"2010","journal-title":"Journal of Pure and Applied Algebra"},{"key":"2022121408225653800_ref4","article-title":"Categories with a base of computability","author":"Gambarte","year":"2022"},{"key":"2022121408225653800_ref5","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1215\/ijm\/1256052950","article-title":"Relations in categories","volume":"14","author":"Klein","year":"1970","journal-title":"Illinois Journal of Mathematics"},{"key":"2022121408225653800_ref6","volume-title":"Realizability Toposes and Language Semantics","author":"Longley","year":"1995"},{"key":"2022121408225653800_ref7","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1017\/S0960129507006251","article-title":"On the ubiquity of certain total type structures","volume":"17","author":"Longley","year":"2007","journal-title":"Mathematical Structures in Computer Science"},{"key":"2022121408225653800_ref8","doi-asserted-by":"crossref","first-page":"E240201","DOI":"10.1017\/S0960129513000182","article-title":"Computability structures, simulations and realizability","volume":"24","author":"Longley","year":"2014","journal-title":"Mathematical Structures in Computer Science"},{"key":"2022121408225653800_ref9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-47992-6","volume-title":"Higher-Order Computability","author":"Longley","year":"2015"},{"key":"2022121408225653800_ref10","article-title":"Dependent sums and dependent products in Bishop\u2019s set theory","volume-title":"Types 2018, LIPIcs","author":"Petrakis","year":"2019"},{"key":"2022121408225653800_ref11","volume-title":"Families of Sets in Bishop Set Theory","author":"Petrakis","year":"2020"},{"key":"2022121408225653800_ref12","article-title":"Computability models over categories","author":"Petrakis","year":"2021"},{"key":"2022121408225653800_ref13","first-page":"253","article-title":"Computability models over categories and presheaves","volume-title":"Logical Foundations of Computer Science 2022","author":"Petrakis","year":"2022"},{"key":"2022121408225653800_ref14","volume-title":"Continuity and Effectiveness in Topoi","author":"Rosolini","year":"1986"},{"key":"2022121408225653800_ref15","volume-title":"Category Theory in Context","author":"Riehl","year":"2016"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/8\/1815\/47846268\/exac077.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/8\/1815\/47846268\/exac077.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T11:43:22Z","timestamp":1671018202000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/32\/8\/1815\/6794241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,9]]},"references-count":15,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,11,9]]},"published-print":{"date-parts":[[2022,12,9]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exac077","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,12]]},"published":{"date-parts":[[2022,11,9]]}}}