I would like to call a semigroup without an identity a "pure semigroup" and a semigroupoid without any identity a "pure semigroupoid". I'm not sure whether such things have been defined in literature before so may I ask whether accepted terms for such things already exist..thank you very much!
2026-03-27 19:40:24.1774640424
Do we have accepted terms for semigroups and semigroupoids without identities?
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A semigroup is just a set with an associative binary relation, not necessarily with identity. A semigroup with identity is called a monoid.