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Let A be a finitely generated connected graded k-algebra defined by a finitenumber of monomial relations. Then there is a finite directed graph, Q, theUfnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) areequivalent: QGr(A) denotes the quotient category of graded A-modules modulo thesubcategory consisting of those that are the sum of their finite dimensionalsubmodules; QGr(kQ) has a similar definition. The proof makes use of an algebrahomomorphism A--->kQ that may be of independent interest.

An equivalence of categories for graded modules over monomial algebras and path algebras of quivers