We give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [H. Krause, Approximations and adjoints in homotopy categories, Math. Ann. 353 (2012), 765–781]. Then we provide a criterion for the existence of r...

Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with stochastic process languages. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is ...

We prove that the following two categories of sl(n,C)-modules are equivalent: 1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; 2) the category of all subquotients of modules F ⊗ M , where F is a finite-dimensional module and M is a fixed simple generic Gelfand-Zetlin module with integral central c...

A result by Curien establishes that filiform concrete data structures can be viewed as games. We extend the idea to cover all stable concrete data structures. This necessitates a theory of games with an equivalence relation on positions. We present a faithful functor from the category of concrete data structures to this new category of games, allowing a game-like reading of the former. It is po...

The relationship of bisimilarity, logical and behavioral equivalence to each other is wellresearched for the interpretation of modal logics through stochastic Kripke models. It can be shown that two Kripke models are bisimilar (i.e. they are related through a span of morphisms) iff they are behavioral equivalent (i.e., they are related through a cospan), which in turn is equivalent to their bei...

We fill a gap in the literature regarding ‘transport of structure’ for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing (classical higher) homological algebra. As an application our main results, we show that skeleton one these kinds inherits same structure canonical way, up to equivalence. In particular, it follows weak (n+2)-angulated category is fact what call stron...

Poincar\'e maps and suspension flows are examples of fundamental constructions in the study dynamical systems. This aimed to show that these define an adjoint pair functors if categories systems suitably set. First, we consider construction category on topological manifolds, which not necessarily smooth. We well-known results can be generalized is functorial, a with global sections adequately d...

It was shown by Ostrik (Int. Math. Res. Not. 2003(27), 1507–1520 2003) and Natale (SIGMA Symmetry Integrability Geom. Methods Appl. 13, 042 2017) that a collection of twisted group algebras in pointed fusion category serve as explicit Morita equivalence class representatives indecomposable, separable such categories. We generalize this result constructing group-theoretical This is achieved prov...

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

We generalize the notion of an MV-algebra in the context of residuated lattices to include noncommutative and unbounded structures. We investigate a number of their properties and prove that they can be obtained from lattice-ordered groups via a truncation construction that generalizes the Chang–Mundici Γ functor. This correspondence extends to a categorical equivalence that generalizes the one...