I realize this is an old question. I decided to answer it anyway. OP is probably gone but others may benefit.
Fuse size cannot be discussed without discussing wire size. The purpose of the fuse is to prevent wiring from getting too hot. If the wire gets too hot it may cause burns to people who touch it or even cause the insulation to smoulder or burn. It can even start a fire. Fuses protect against that.
To figure out how large the wire needs to be consult an ampacity table (use a search engine). From the cerrowire website ampacity table I see that for 80 Amps you would need 3 AWG wire. But I have never seen 3 AWG wire. So I recommend you use 2 AWG (equivalent to 6.5mm diameter) wire. You can use a 100 Amp fuse.
There is one more thing. Fuses have a maximum interrupt rating. Fuses do not operate instantly. The fault current must be in excess of the fuse rating for some period of time before the fuse will blow. The higher the fault current, the faster the fuse will blow. But if the fault current is extremely high, a physically small fuse may explode when it blows. Theoretically it may even fail to open the circuit due to arcing or something. With lead acid batteries, the potential fault current may be several hundred Amps. So you should select a fuse with an interrupt rating of at least 1000 Amps.
If the wire has to run a long way, you may need to use heavier wire to avoid excessive voltage drop under maximum load. That is fine. You can still use the 100 A fuse with larger wire. If you want to learn about voltage drop, pose a separate question.
Note: the wire to the solar panels will likely be much smaller diameter. So you need to put a separate fuse in series with those smaller wires, sized based on their diameter.