Let me try it this way. This is written for macro students, and their teachers. But it's aimed at researchers too. It's about the role of money in macro models.
Ignore what New Keynesian macroeconomists say about their own models. Listen to me instead.
Start with the second-year textbook ISLM model. The price level P is fixed, so real and nominal interest rates R are the same thing. The nominal money supply M is also fixed. Which means the real money supply M/P is fixed too, and the LM curve slopes up. And the IS curve slopes down.
How could we convert that standard ISLM model into a New Keynesian model?