From free idempotent monoids to free multiplicatively idempotent rigs

Abstract

A multiplicatively idempotent rig (which we abbreviate to mirig) is a rig satisfying the equation r2 = r. We show that a free mirig on finitely many generators is finite and compute its size. This work was originally motivated by a collaborative effort on the decentralized social network Mastodon to compute the size of the free mirig on two generators.