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...

We consider the value 1 problem for probabilistic automata over finite words. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it. The aim of this paper is to prove that one such algorithm, called the Markov Monoid algorithm, is optimal. To this end, we develop a profinite theory for probabilistic automata. This new framework gives a t...

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 ...