How do crossovers affect impedance?

[Bakerman]

I have an amp that is 2 ohm stable, and a component set where the tweeter and mid is 4 ohms. As you know, if i wire them parallel, it takes it down to 2 ohms...now, they came with a crossover...one pos and neg input, one pos and neg mid output, and one pos and neg tweeter output. Do crossovers keep the tweeter and the mid parallel to each other so that it will stay at a 2 ohm impedance, or is this something that varies from name brand, type of speaker, etc? If it is, here is the link to the component set.

Hifonics ZXi6.5C