REPRESENTATIONS OF FINITE DIRECTED CATEGORIES
LIPING LI
Abstract. A finite directed category is a k-linear category with finitely many objects and an underlying poset structure, where k is an algebraically closed field. This concept unifies structures such as k-linerizations of posets and fi- nite EI categories, quotient algebras of finite-dimensional hereditary algebras, triangular matrix algebras, etc. In this paper we study representations of fi- nite directed categories, estimate their global dimensions and finitistic dimen- sions, and discuss their stratification properties. We also show the existence of generalized APR tilting modules for triangular matrix algebras under some assumptions.