"Volitional verb + (よ)う/ましょう" can express the speaker's will to do, invitation or presumption, whereas "non-volitional verb + (よ)う/ましょう" only means presumption "~だろう/でしょう".
e.g.
(行く is volitional.)
あの店にもう一度行こう。= 行くだろう。(presumption)
あの店に(必ず)もう一度行こう。(the speaker's will)
あの店にもう一度(一緒に)行こう。(invitation)
(降る is non-volitional.)
明日雨が降ろう。= 降るだろう。(presumption)
ある is non-volitional, so ありましょう is only used as presumption あるでしょう; There will be a class on Monday. It can't be an invitation.
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