We discuss the use of relation lifting in the theory of setbased coalgebra. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavorial equivalence. On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullbacks, such as the monot...

Namely, the assumption implies that for every prime p, one has induced isomorphisms H∗>n(BH;Z/p) → H∗>n(BG;Z/p) and thus, by applying the “reconstruction functor”, isomorphisms H∗(BH;Z/p)→ H∗(BG;Z/p). Since BG and BH are spaces of finite type, it follows that the induced map H∗(BH;Z)→ H∗(BG;Z) is an isomorphism too. Thus, by Jackowski [6] and Minami [10], ρ is an isomorphism of Lie groups. In s...

Let X be a projective scheme over a noetherian base scheme S, and let F be a coherent sheaf on X. For any coherent sheaf E on X, consider the set-valued contravariant functor Hom(E,F) on S-schemes, defined by Hom(E,F)(T ) = Hom(ET ,FT ) where ET and FT are the pull-backs of E and F to XT = X ×S T . A basic result of Grothendieck ([EGA] III 7.7.8, 7.7.9) says that if F is flat over S then Hom(E,...

The articles [28], [32], [2], [15], [1], [5], [6], [4], [31], [16], [29], [17], [27], [13], [3], [25], [26], [10], [11], [8], [30], [14], [20], [18], [12], [23], [22], [24], [7], [9], [19], and [21] provide the notation and terminology for this paper. In this paper n denotes a natural number. Let C be a simple closed curve. The functor UpperAppr(C) yields a sequence of subsets of the carrier of...

The papers [28], [32], [2], [15], [1], [5], [6], [4], [31], [16], [29], [17], [27], [13], [3], [25], [26], [10], [11], [8], [30], [14], [20], [18], [12], [23], [22], [24], [7], [9], [19], and [21] provide the terminology and notation for this paper. In this paper n denotes a natural number. Let C be a simple closed curve. The functor UpperAppr(C) yields a sequence of subsets of the carrier of E...

We take the point of view that, if transition systems are coalgebras for a functor T, then an adequate logic for these transition systems should arise from the ‘Stone dual’ L of T. We show that such a functor always gives rise to an ‘abstract’ adequate logic for T-coalgebras and investigate under which circumstances it gives rise to a ‘concrete’ such logic, that is, a logic with an inductively ...

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

Coalgebras for a functor T on a category X model many different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary strongly complete specification languages for Set-based coalgebras. We show how to associate a finitary logic to any finite-sets preserving functor T and prove the logic to be strongly complete under a mild condition on T . The proof i...

the ordinary tensor product of modules is defined using bilinear maps (bimorphisms), that are linear in eachcomponent. keeping this in mind, linton and banaschewski with nelson defined and studied the tensor product in an equational category and in a general (concrete) category k, respectively, using bimorphisms, that is, defined via the hom-functor on k. also, the so-called sesquilinear, or on...