A key component of inflation that is almost always overlooked is something called "the velocity of money"....Just so since the crash of 2008. The velocity of money slowed considerably. Which is precisely why the Fed has been printing so much more of it. The Fed is attempting to get more cash out there to increase the sluggish movement of money.
Put more money into more hands and some of it is going to move around.
The traditional measures of velocity of money are outdated in that they are too narrow. When we talk about "money" now we must consider things like collateral and collateral chains.
OK, the big problem here is that the basic monetary identity PY=MV (where P is a price vector, Y is an output vector, M is a scalar measure of money supply, and V is a scalar "velocity of money")is an accounting identity and not a function. If you treat all four variables as dependent variables, the system is overdetermined. You set three as dependent variables to be explained with a function and the fourth (V) automatically comes out in the wash. You don't need a "theory" for the velocity of money. If you have one, you need to identify which other part of the identity has become the residual (price level? output? money supply?). The options don't look very attractive.
This is why a lot of monetary theory texts express the identity as V=(PY)/M, which makes clear that V is arrived at as a definition, not a function.
The statement that increases in the money supply cause prices to rise (inflation) is just another restatement of this monetary identity with the added assumption that increases in the money supply have no direct effect on output or velocity. This is where an explanatory "theory of velocity of money" might come in, but it would be a theory derived from a theory of prices and output.
Also note that if we are in a Keynesian liquidity trap, increases in the money supply are not inflationary because the velocity of money changes (through hoarding) to offset the increases in monetary base. Almost every conservative (or monetarist) economist in 2009 predicted rapid inflation which did not occur. This "natural experiment" should have been the definitive proof that we were in a liquidity trap and that the macro dynamics were very close to the 1928--1933 experience. It's a measure of the collective denial of much of the profession that five years out almost all of these false predictors stand by there model and persist in recommending ruinous policies based on wishful thinking and economic theory that comes out of a CrackerJack box.
So I take it you disagree with my point that what counts as money is too narrowly defined?