3 ms·
Side note: the study of monoids isn't a very big field in mathematics, because they're too simple to say too much about them. But if you modify them just a bit,
by shigeo 6y ago
Side note: the study of monoids isn't a very big field in mathematics, because they're too simple to say too much about them. But if you modify them just a bit, either in the direction of groups or in the direction of categories, you get massive fields of study.
- OscarCunningham 6y agoI'm reminded of John Baez writing recently (https://twitter.com/johncarlosbaez/status/1246470112321953792 https://twitter.com/johncarlosbaez/status/124647011232195379...) about commutative semigroups. Even simpler, but still lots to say!
- shigeo 6y agoI probably still stand corrected, but commutativity is a much stronger condition than the existence of an identity!
- OscarCunningham 6y agoI think the existence of an identity isn't very important. You can adjoin an identity to any semigroup to turn it into a monoid. In any case, doesn't adding more properties make a theory simpler? For example the classification of finite simple groups is much harder than the classification of finite simple commutative groups.