To me, this is interesting as an example of a category in the intersection of "elementary topos" and "finitary algebraic" but which is not equivalent to "category of M-sets" for any monoid M (or at least not equivalent as concrete categories). As a finitary algebraic category, it is described by two unary operations l,r and a binary operation m with the identities l(m(x,y))=x, r(m(x,y))=y, m(l(x),r(x))=x.
This issue has been created by Daniel Schepler via the submission form on https://catdat.app/categories
To me, this is interesting as an example of a category in the intersection of "elementary topos" and "finitary algebraic" but which is not equivalent to "category of M-sets" for any monoid M (or at least not equivalent as concrete categories). As a finitary algebraic category, it is described by two unary operations l,r and a binary operation m with the identities l(m(x,y))=x, r(m(x,y))=y, m(l(x),r(x))=x.
This issue has been created by Daniel Schepler via the submission form on https://catdat.app/categories