It's not inflation.
Yes, the Fed's quantative easing has helped (buying bonds and debt). It's also a handful of companies that are crushing it right now (Apple, Amazon, Google, Facebook, etc.), and they are doing much of the updward market driving. There also are some micro-bubbles out there (electric vehicles and alternative energy stocks). There is also the stimulus that had put $2400/month in people's hands. There are also the retail investors (gamblers and folks like you and me) that have been buying a lot of stocks, including moves that are hard to understand such as buying Kodak and Hertz and failing to grasp that a stock split is a non-event but buying it anyway. And, related to the Fed, the fact that the real, post-inflation return on Treasuries is negative has lead a lot of investors to buy riskier products (equities and corporate debt).
So, there are a lot things driving up the equity markets these days. Can it last? If no, will it just flatten, dip 10%, or crash? It's guesswork. Stick to your investment plan and we all should be fine.