We sketch a theory of divisibility and factorization in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely topologized topological monoids. We define the topological factorization monoid, a generalization of the factorization monoid for algebraic monoids, and show that it is always topologically...

We aim to reconstruct a monoid scheme X from the category of quasi-coherent sheaves over it. This is much in vein Gabriel's original reconstruction theorem. Under some finiteness condition on schemes X, we show that localisations topos Qc(X) are one-to-one correspondence with open subsets while elements correspond points Qc(X). allows us

Tall–Wraith monoids were introduced in [SW09] to describe the algebraic structure on the set of unstable operations of a suitable generalised cohomology theory. In this paper we begin the study of Tall–Wraith monoids in an algebraic and categorical setting. We show that forV a variety of algebras, applying the freeV-algebra functor to a monoid in Set produces a Tall–Wraith monoid. We also study...

This paper concerns residuated lattice-ordered idempotent commutative monoids that are subdirect products of chains. An algebra of this kind is a generalized Sugihara monoid (GSM) if it is generated by the lower bounds of the monoid identity; it is a Sugihara monoid if it has a compatible involution ¬. Our main theorem establishes a category equivalence between GSMs and relative Stone algebras ...