when studying russian morphology, one can distinguish two categories. these categories are “grammatical” and “lexico-grammatical”. grammatical categories can be specified through a series of grammatical features of words. considering different criteria, russian grammarians and linguists divide grammatical categories of their language into different types. in determining lexico-grammatical types...

This is the first in a series of papers which we study representations Brauer category and its allies. We define general notion triangular that abstracts key properties decomposition semisimple complex Lie algebra, develop highest weight theory for them. show category, partition number related diagram categories admit this structure.