Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 2. In our paper, we investigate the coalgebraic equivalence notions of 2-bisimulation, behavioural equivalence and neighbourhood bisimulation (a notion based on pus...

For an associative ring R, let P be an R-module with S = EndR(P). C. Menini and A. Orsatti posed the question of when the related functor HomR(P, −) (with left adjoint P ⊗S −) induces an equivalence between a subcategory of R M closed under factor modules and a subcategory of S M closed under submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphi...

We study the biclosedness of monoidal categories modules and comodules over a (left or right) Hopf algebroid, along with their bimodule category centres respective opposite corresponding categorical equivalence to anti Yetter-Drinfel’d contramodules modules, respectively. This is directly connected existence trace functor on in question, which turn allows recover (or define) cyclic operators en...

Abstract. Let G be a group of automorphisms of a category C. We give a definition for a functor F : C → C to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finitedimensional categories with group G whose action on C is free and locally bonded. Here C/G is defined for any category C and does not require that the act...

Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the pap...

The branching space of a flow is the topological space of germs of its nonconstant execution paths beginning in the same way. However, there exist weakly Shomotopy equivalent flows having non weakly homotopy equivalent branching spaces. This topological space is then badly behaved from a computer-scientific viewpoint since weakly S-homotopy equivalent flows must correspond to higher dimensional...

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the...

Rickard proved that for certain self-injective algebras, a stable equivalence induced from an exact functor is of Morita type, in the sense Broué. In this paper we study singular equivalences finite-dimensional algebras tensor product functors. We prove Gorenstein tensoring with suitable complex bimodules induces type level, Wang. This recovers Rickard's theorem case.

// P0(F ), where Pn(F ) is the universal n-excisive or n-polynomial approximation to F [Goo03]. Setting F = id, a theorem of Goodwillie asserts that the natural map X → holimPn(id)(X) is a weak equivalence for X simply connected. Thus, it is of interest to understand the layers Dn(F ) := fib (Pn(F )→ Pn−1(F )) . This functor is an n-homogeneous functor, and these are completely classified. Theo...

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings – Noetherian semirings, natural numbers – are proper. Properness matters as the equivalence problem for weighted automata over a semiring which is proper and finitely and effectively presented is decidable. Milius generalised the notion of properness from a semiring to a functor. As...