Normal orthogonality spaces

An orthogonality space is a set X together with symmetric and irreflexive binary relation ⊥, called the relation. A block partition of maximal mutually orthogonal elements X, decomposition collection subsets each which complement union others. (X,⊥) normal if any gives rise to unique space. The one-dimensional subspaces Hilbert equipped usual provides motivating example. Together maps that are, in natural sense, compatible formation decompositions from partitions, spaces form category, denoted by NOS. objective present paper characterise both objects morphisms NOS various perspectives as well compile basic categorical properties