Any mixer can be used as up- or down-converter. In a mixer, a non-linear element is "pumped" by a local-oscillator signal, and generates harmonics. If another signal is added (most often with a lower power than LO is), harmonic combinations of both signal frequencies are generated.
Then we use various filters to utilize some of the generated signals while others are suppressed. A mixer then has a "conversion loss" which indicates how well we transferred one signal at a chosen frequency into another one at another frequency.
If e.g. an IF frequency of 1 MHz is upconverted to 3 MHz, we can use a local oscillator running at 2 or 4 MHz. In receivers, we use mostly down converters, then they can convert either one or two side bands to the IF.
Their noise figure depends if the "image" filter is used (single-sideband conversion ), or not (DSB, double-sideband conversion). Noise figure of a DSB mixer is one-half of that of a SSB mixer, but DSB mixers are rather used in receivers processing noise while SSB mixers are used to process human-generated signals.'
Similar rules are valid also if a receiver utilizes an upconverter (some HF receivers do). Among communication engineers there still is a confusion about how the noise is processed in mixers.
Radio astronomers who process noise in their receivers mostly use DSB mixers, and there is no confusion about their noise performance.
---------- Post added at 19:20 ---------- Previous post was at 19:16 ----------
One good reference is :
www.agilent.com/find/eesof, another,
www.deetc.jsel.ipl.pt, chapter 12. A bad reference just appeared in Microwaves &RF, Jan.2012, pp.86-89. Mr.Monzello simply never understood the Friis' formula for noise in receivers.