[来る] → こよう
Polite form: [verb stem] + ましょう
The 意向形 (volitional form) is used to express a speaker's will or intention to do something, or to suggest or invite someone to do something together. It is equivalent to "let's ~" or "I'll ~" / "shall we ~" in English.
Godan (V5) verbs: Change the final う-column kana to the corresponding お-column kana and add う.
The polite equivalent is 〜~ましょう (V[stem] + ましょう).
The most common use of the volitional form is to propose doing something together with the listener.
Adding か to the polite volitional makes a polite invitation or suggestion ("shall we ~?"):
When used by itself (often as an inner thought or casual statement), it expresses the speaker's intention or decision.
~ようと思う – "I think I'll ~" / "I'm planning to ~". Used to express a softer or more considered intention.
~ようとする – "to try to ~" / "to be about to ~". Describes an attempt or the moment just before an action.
The plain volitional (e.g. いこう行こう) is casual and used with friends or family. The polite form 〜~ましょう (e.g. いきましょう行きましょう) is appropriate in formal situations or with people you are not close to.