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- W2969932740 abstract "For a monoid $M$, we denote by $mathbb G(M)$ the group of units, $mathbb E(M)$ the submonoid generated by the idempotents, and $mathbb G_L(M)$ and $mathbb G_R(M)$ the submonoids consisting of all left or right units. Writing $mathcal M$ for the (monoidal) category of monoids, $mathbb G$, $mathbb E$, $mathbb G_L$ and $mathbb G_R$ are all (monoidal) functors $mathcal Mtomathcal M$. There are other natural functors associated to submonoids generated by combinations of idempotents and one- or two-sided units. The above functors generate a monoid with composition as its operation. We show that this monoid has size $15$, and describe its algebraic structure. We also show how to associate certain lattice invariants to a monoid, and classify the lattices that arise in this fashion. A number of examples are discussed throughout, some of which are essential for the proofs of the main theoretical results." @default.
- W2969932740 created "2019-08-29" @default.
- W2969932740 creator A5069552429 @default.
- W2969932740 date "2019-08-22" @default.
- W2969932740 modified "2023-10-15" @default.
- W2969932740 title "Idempotents and one-sided units: Lattice invariants and a semigroup of functors on the category of monoids" @default.
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