We consider Rabin’s Monadic Second Order logic (MSO) of the full binary tree extended with Harvey Friedman’s “for almost all” second-order quantifier (∀∗) with semantics given in terms of Baire Category. In Theorem 1 we prove that the new quantifier can be eliminated (MSO+∀∗ =MSO). We then apply this result to prove in Theorem 2 that the finite–SAT problem for the qualitative fragment of the pr...

The category HopfC of Hopf monoids in a symmetric monoidal category C, assumed to be locally finitely presentable as a category, is analyzed with respect to its categorical properties. Assuming that the functors “tensor squaring” and “tensor cubing” on C preserve directed colimits one has the following results: (1) If, in C, extremal epimorphisms are stable under tensor squaring, then HopfC is ...

Seese’s conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show to establish this it would suffice grids size can be interpreted in two families classes: minimal hereditary clique-width; and antichains clique-width under the induced subgraph relation. explore currently known former category indeed them.

This paper presents the semantics of database mappings in the relational database (DB) category, based on the power-view monad T and monadic algebras. The semantics can be interpreted as a computational model of viewbased mappings between databases, where each query (view-mapping) can be seen as a program, so that we can use the paradigm ”from values to computations”. The objects in this catego...

After recalling the definition of a bicoalgebroid, we define comodules and modules over a bicoalgebroid. We construct the monoidal category of comodules, and define Yetter–Drinfel’d modules over a bicoalgebroid. It is proved that the Yetter–Drinfel’d category is monoidal and pre–braided just as in the case of bialgebroids, and is embedded into the one–sided center of the comodule category. We p...

We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois desce...

The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting monad. A complication of this approach is that the operations associated to the pre-existing monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system Fω. Her...

We describe a simplified categorical approach to Galois descent theory. It is well known that Galois descent is a special case of Grothendieck descent, and that under mild additional conditions the category of Grothendieck descent data coincides with the Eilenberg-Moore category of algebras over a suitable monad. This also suggests using monads directly, and our monadic approach to Galois desce...

Monads, proposed by Moggi [16] of their use in structuring denotational descriptions and then popularized by Wadler[21], are becoming an increasingly important tool for structural functional programming[8, 10, 11]. The reason is that monads provide a uniform framework for describing a wide range of programming language features including, for example, state, I/O, continuations, exceptions, pars...