# range resolution FMCW radar influenced by Nyquist?

I am puzzled about this for some time now. According to theory, the max range of a FMCW radar in practice is limited by the sampling frequency

$$R_{max} = \frac{c_0 T_{upchirp}}{2 f_{BM}}f_s$$

Since one has to obey the Nyquist sampling theorem, this range halves so that

$$R_{max} = \frac{c_0 T_{upchirp}}{2 f_{BM}}\frac{f_s}{2}$$

I know that the range resolution is

$$\Delta R = \frac{c_0}{2 f_{BW}}$$ which effectively defines range gates after the FFT.

Also it holds that $$R_{max} = \frac{\Delta R\,N}{2}$$ where N is the number of sample points in for the time series of the beat frequency. This ultimately means that the upper half of the FFT is discarded, correct? Is this view the same than only considering the lower half of any FFT due to duplicated but mirrored information?

My main question though is, does that mean, that the number of range bins, which is equal to N, is cut in half or the resolution itself?

I am having trouble getting the deeper meaning of this equation and appreciate help.