Non-symmetric Orthogonal Geometry of Mukai Lattices

In this Section, companion of the previous one, we discuss properties of classes of the exceptional objects of a triangulated category \(\mathscr D\) in its Grothendieck group \(K_0(\mathscr D)\) , the exceptional bases. This can be interpreted as a sort of linearization procedure, translating objects of an abstract category into elements of a more elementary algebraic structure (a lattice or vector space), more suitable for explicit computations.