increasing output voltage of a schmitt trigger op amp
This might not be exactly right, but because the comparator has an open-drain output, you have to think of it as being something resembling the device surrounded by the dashed box:







simulate this circuit &ndash; Schematic created using CircuitLab

When M1 is off (high output), the voltage at OUT is determined by the R1/R2 voltage divider. An open drain output does not drive a high voltage. Instead, it shuts off to a high impedance state, and the high voltage is created by a pull-up resistor (either supplied by you, or perhaps one that is provided in internally ("weak pullup" type feature)).

If you look at the hysteresis example in the datasheet, it works differently. The output is bootstrapped from the input. If we draw it with our explicit open drain model, it looks like this:







simulate this circuit

So here, if OA1 cuts off the output transistor, then OUT is at the same voltage as IN. It is pulled up to IN by the two resistors. And of course if the transistor is fully on, then OUT is pulled to ground.