If a Quillen model category can be specified using a certain logical syntax (intuitively, “is algebraic/combinatorial enough”), so that it can be defined in any category of sheaves, then the satisfaction of Quillen’s axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric mo...

The modalities and© of necessary and lax truth described by Pfenning and Davies can be seen to arise from the same pair of adjoint logical operators F and U , which pass in both directions between two judgments of differing strength. This may be generalized to a logic with many such adjunctions, across judgments subject to different substructral disciplines, allowing explanation of possibility ...

We develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-adjoint functor. This construction generalizes the known adjunctions for the categories of Doi-Hopf modules and entwining structures. The separability of the induction and a...

We study Hopf monoids in entropic semi-additive varieties (equivalently, entropic Jónsson-Tarski varieties and categories of semimodules over a commutative semiring, respectively) with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor. These investigations are based on the concept of the abelian core of a semi-additive variety variety and its ...

There exists a direct relation between fuzzy rough sets and fuzzy preorders. On the other hand, it is well known the existing parallelism between Formal Concept Analysis and Rough Set Theory. In both cases, Galois connections play a central role. In this work, we focus on adjunctions (also named isotone Galois connections) between fuzzy preordered sets; specifically, we study necessary conditio...

We describe a rational algorithm for nding the denominator of any solution of a linear ordinary diierential equation in its coeecient eld. As a consequence, there is now a rational algorithm for nding all such solutions when the coeecients can be built up from the rational functions by nitely many algebraic and primitive adjunctions. This also eliminates one of the computational bottlenecks in ...

A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is re-examined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete under...

The purpose of this paper is to collect the homotopical methods used in the development of the theory of flows initialized by author’s paper “A model category for the homotopy theory of concurrency”. It is presented generalizations of the classical Whitehead theorem inverting weak homotopy equivalences between CW-complexes using weak factorization systems. It is also presented methods of calcul...