Abstract We construct and study projective Reedy model category structures for bimodules infinitesimal over topological operads. Both produce the same homotopy categories. For categories in question, we build explicit cofibrant fibrant replacements. show that these are right proper under some conditions left proper. also extension/restriction adjunctions.

We define and study LNL polycategories, which abstract the judgmental structure of classical linear logic with exponentials. Many existing structures can be represented as including adjunctions, exponential comonads, multicategories, IL-indexed categories, linearly distributive categories storage, commutative strong monads, CBPV-structures, models polarized calculi, Freyd-categories, skew well ...

In this paper we regard languages and their acceptors – such as deterministic or weighted automata, transducers, or monoids – as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: a) We provide sufficient conditions on the output category so that minimization of the corresponding a...

This paper investigates expressivity of modal logics for transition systems, multitransition systems, Markov chains, and Markov processes, as coalgebras of the powerset, finitely supported multiset, finitely supported distribution, and measure functor, respectively. Expressivity means that logically indistinguishable states, satisfying the same formulas, are behaviourally indistinguishable. The...

The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues relate...

In the setting of enriched category theory, we describe dual adjunctions of the form L R : Spa −→ Alg between the dual of the category Spa of “spaces” and the category Alg of “algebras” that arise from a schizophrenic object , which is both an “algebra” and a “space”. We call such adjunctions logical connections. We prove that the exact nature of is that of a module that allows to lift optimall...

Module systems embed elements of methodologies, formalisms and tools for programming-in-the-large into programming languages. In our thesis we design a module system, its categorical model and a constructive semantics of the system in the model. The categorical model is simple and general, built using elementary categorical notions, admitting many variants and extensions of the module system. O...

Consider categories with involutions which fix objects, functors which preserve involution, and natural transformations. In this setting certain natural adjunctions become universal and, thereby, become constructible from abstract data. Although the formal theory of monads fails to apply and the Eilenberg-Moore category fails to fit, both are successfully adapted to this setting, which is a 2-c...