By constructions in monoid and group theory we exhibit an adjunction between the category of partially ordered monoids and lazy monoid homomorphisms, and the category of partially ordered groups and group homomorphisms, such that the unit of the adjunction is injective. We also prove a similar result for sets acted on by monoids and groups. We introduce the new notion of lazy homomorphism for a...

Let E be an ample rank r bundle on a smooth toric projective surface, S, whose topological Euler characteristic is e(S). In this article, we prove a number of surprisingly strong lower bounds for c1(E) and c2(E). First, we show Corollary (3.2), which says that, given S and E as above, if e(S) ≥ 5, then c1(E) ≥ r2e(S). Though simple, this is much stronger than the known lower bounds over not nec...

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.