WordNet sense 1 (insist on having one's opinions and rights recognized):

assert

WordNet sense 2 (summon into action or bring into existence, often as if by magic):

arouse, conjure, evoke, invoke, raise, stir, bring up, call down, conjure up, call forth

WordNet sense 3 (cause to protrude or as if to protrude):

stick

WordNet sense 4 (propose as a candidate for some honor):

nominate, put up

WordNet sense 5 (put before):

posit, state, submit