Monetary policy mainly affects demand-pull inflation through directly raising aggregate demand. It has a minor impact on cost-push as borrowed finance may be considered an input for a product e.g. if the cost of borrowing goes up a firm that has a highly geared capital structure may need to raise prices. It indirectly affects imported inflation as changes in MP (loosening depreciates) (tightening appreciates) the dollar, thereby affecting the price of imports, though not significantly. And MP does have a sizeable impact on inflationary expectations, however, inflationary targeting has effectively negated this. I would say arguments could be made for all of them, but my inclination would be cost-push as MP works the demand-side of the economy and cost-push inflation is a supply side problem.
