One key thing missing out from many peoples understanding is the strength of currency. Perhaps less applicable to the US, but if your country has low interest rates demand for its currency reduces and then imports increase in price. If non elastic goods like fuel and food are imported, this drives inflation.

If you have high interest rates and that leads to increased demand for currency then your imports will be cheaper and thus inflation lower.

However that stronger currency reduces demand for exported goods, so just like domestic policymakers high rates risk reduced demand which leads to recession.

The main problem with a low interest rate environment is that it allows failing companies to artificially stay afloat, using resources (workers, fuel, goods) better deployed elsewhere.