Is it considered a fundamental axiom among economists that higher rates = downward inflation?

This is what I was taught, and I still believe it.

To provide a few historical examples:

It isn’t mere coincidence that the Fed began rapidly increasing interest rates in 1979, only to be followed by inflation peaking in 1980 and then precipitously plummeting.

More recently, when inflation spiked during Covid, the exact same sequence occurred. The Fed cranked up interest rates and inflation began to subside.

If we allow for the fact that there is a time delay in consequence, am I correct to assume as a fundamental axiom that, in economic theory, the relationship between interest rates and inflation is as causally connected as anything else in the field?