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@article{1800684,
author = {Paseka, Jan and Vetterlein, Thomas},
article_number = {3},
doi = {http://dx.doi.org/10.1016/j.jpaa.2021.106859},
keywords = {Orthogonality spaces; Undirected graphs; Categories; Boolean subalgebras; Linear orthogonality spaces; Generalised semilinear map},
language = {eng},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
title = {Categories of orthogonality spaces},
url = {https://doi.org/10.1016/j.jpaa.2021.106859},
volume = {226},
year = {2022}
}
TY - JOUR
ID - 1800684
AU - Paseka, Jan - Vetterlein, Thomas
PY - 2022
TI - Categories of orthogonality spaces
JF - Journal of Pure and Applied Algebra
VL - 226
IS - 3
SP - 106859
EP - 106859
PB - Elsevier B.V.
SN - 00224049
KW - Orthogonality spaces
KW - Undirected graphs
KW - Categories
KW - Boolean subalgebras
KW - Linear orthogonality spaces
KW - Generalised semilinear map
UR - https://doi.org/10.1016/j.jpaa.2021.106859
N2 - An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a Boolean algebra. Together with the maps that preserve the Boolean substructures, we are led to the category NOS of normal orthogonality spaces. Moreover, an orthogonality space of finite rank is called linear if for any two distinct elements e and f there is a third one g such that exactly one of f and g is orthogonal to e and the pairs e, f and e, g have the same orthogonal complement. Linear orthogonality spaces arise from finite-dimensional Hermitian spaces. We are led to the full subcategory LOS of NOS and we show that the morphisms are the orthogonality-preserving lineations. Finally, we consider the full subcategory OS pound of LOS whose members arise from positive definite Hermitian spaces over Baer ordered *-fields with a Euclidean fixed field. We establish that the morphisms of OS pound are induced by generalised semiunitary mappings.
ER -
PASEKA, Jan a Thomas VETTERLEIN. Categories of orthogonality spaces. \textit{Journal of Pure and Applied Algebra}. Elsevier B.V., 2022, roč.~226, č.~3, s.~106859-106880. ISSN~0022-4049. Dostupné z: https://dx.doi.org/10.1016/j.jpaa.2021.106859.
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