Step 1: Understand coagulation of lyophobic sols.
Coagulation is the process of destabilization of colloidal particles leading to aggregation and precipitation. It generally occurs by removing charge stabilization.
Step 2: Analyze electrophoresis (II).
In electrophoresis, colloidal particles move under electric field and are discharged at electrodes, leading to neutralization and coagulation. Hence it is a valid method.
Step 3: Analyze mixing oppositely charged sols (III).
When positively and negatively charged sols are mixed, charge neutralization occurs, causing aggregation and precipitation. This is called mutual coagulation.
Step 4: Analyze cooling (I).
Cooling mainly affects solubility and stability but is not a standard method for coagulation of lyophobic sols. Hence incorrect here.
Step 5: Analyze dialysis (IV).
Dialysis is used for purification of sols by removing ions, not for coagulation. So it is also incorrect.
Step 6: Final conclusion.
Only electrophoresis and mixing of oppositely charged sols are valid coagulation methods.
Final Answer:
\[
\boxed{\text{II, III}}
\]