论文标题
正交空间的类别
Categories of orthogonality spaces
论文作者
论文摘要
正交空间是配备对称和反射性二进制关系的集合。我们认为任何相互正交元件的额外特性都会产生布尔代数的结构。加上保留布尔结构的地图，我们被带到了普通正交性空间的类别$ {\ Mathcal n} {\ Mathcal O} {\ Mathcal S} $。此外，如果任何两个不同的元素$ e $和$ f $都有有限排名的正交空间称为线性，则有第三个$ g $，因此$ f $ and $ g $中的一个正是与$ e $矫正的，而pairs $ e，f $ e，f $和$ e，g $，g $，g $具有相同的正交补充。线性正交空间来自有限维遗产空间。我们被带到了完整的子类别$ {\ MATHCAL L} {\ MATHCAL O} {\ MATHCAL S} $ of $ {\ MATHCAL N} {\ MATHCAL N} {\ MATHCAL O} {\ MATHCAL O} {\ MATHCAL S} $，我们表明形态上的形态是Orthogogonsity intogogonsity lineations。最后，我们考虑$ {\ Mathcal l} {\ Mathcal l} {\ Mathcal L} {\ Mathcal l} {\ Mathcal O} {\ Mathcal O} {\ Mathcal o} {\ Mathcal s} $的完整子类别$ {\ Mathcal E} {\ Mathcal O} {\ Mathcal s} $的成员源于Baer of Baer of baer of的积极确定空间$ \ \ sare的n.我们确定$ {\ Mathcal E} {\ Mathcal O} {\ Mathcal S} $的形态是由广义的半统一映射引起的。
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 structures, we are led to the category ${\mathcal N}{\mathcal O}{\mathcal S}$ 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 ${\mathcal L}{\mathcal O}{\mathcal S}$ of ${\mathcal N}{\mathcal O}{\mathcal S}$ and we show that the morphisms are the orthogonality-preserving lineations. Finally, we consider the full subcategory ${\mathcal E}{\mathcal O}{\mathcal S}$ of ${\mathcal L}{\mathcal O}{\mathcal S}$ whose members arise from positive definite Hermitian spaces over Baer ordered $\star$-fields with a Euclidean fixed field. We establish that the morphisms of ${\mathcal E}{\mathcal O}{\mathcal S}$ are induced by generalised semiunitary mappings.
