تقرير
Monadic ortholattices: completions and duality
| العنوان: | Monadic ortholattices: completions and duality |
|---|---|
| المؤلفون: | Harding, John, McDonald, Joseph, Peinado, Miguel |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Quantum Physics |
| مصطلحات موضوعية: | Mathematics - Logic, Quantum Physics, 06C15, 06B23 06E15 |
| الوصف: | We show that the variety of monadic ortholattices is closed under MacNeille and canonical completions. In each case, the completion of $L$ is obtained by forming an associated dual space $X$ that is a monadic orthoframe. This is a set with an orthogonality relation and an additional binary relation satisfying certain conditions. For the MacNeille completion, $X$ is formed from the non-zero elements of $L$, and for the canonical completion, $X$ is formed from the proper filters of $L$. The corresponding completion of $L$ is then obtained as the ortholattice of bi-orthogonally closed subsets of $X$ with an additional operation defined through the binary relation of $X$. With the introduction of a suitable topology on an orthoframe, as was done by Goldblatt and Bimb\'o, we obtain a dual adjunction between the categories of monadic ortholattices and monadic orthospaces. A restriction of this dual adjunction provides a dual equivalence. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2406.06917Test |
| رقم الانضمام: | edsarx.2406.06917 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |