Categories of Orthosets and Adjointable Maps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144414" target="_blank" >RIV/00216224:14310/25:00144414 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10773-025-06031-4" target="_blank" >https://link.springer.com/article/10.1007/s10773-025-06031-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-025-06031-4" target="_blank" >10.1007/s10773-025-06031-4</a>

Result language
angličtina
Original language name
Categories of Orthosets and Adjointable Maps
Original language description
An orthoset is a non-empty set together with a symmetric and irreflexive binary relation perp, called the orthogonality relation. An orthoset with 0 is an orthoset augmented with an additional element 0, called falsity, which is orthogonal to every element. The collection of subspaces of a Hilbert space that are spanned by a single vector provides a motivating example. We say that a map f :X rightarrow Y between orthosets with 0 possesses the adjoint g :Y rightarrow X if, for any x in X and y in Y, f(x) perp y if and only if x perp g(y). We call f in this case adjointable. For instance, any bounded linear map between Hilbert spaces induces a map with this property. We discuss in this paper adjointability from several perspectives and we put a particular focus on maps preserving the orthogonality relation. We moreover investigate the category mathcal{O}mathcal{S} of all orthosets with 0 and adjointable maps between them. We especially focus on the full subcategory mathcalligra {i}mathcal{O}mathcal{S} of irredundant orthosets with 0. mathcalligra {i}mathcal{O}mathcal{S}can be made into a dagger category, the dagger of a morphism being its unique adjoint. mathcalligra {i}mathcal{O}mathcal{S} contains dagger subcategories of various sorts and provides in particular a framework for the investigation of Hilbert spaces.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Project
<a href="/en/project/GF25-20013L" target="_blank" >GF25-20013L: Orthogonality and Symmetry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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