Let X be a finite connected CW-complex of dimension q. If its fundamental group π1(X) is polycyclic of Hirsch number h > q, we show that at least one homotopy group πi(X) is not finitely generated. If h = q or h = q − 1 the same conclusion holds unless X is an Eilenberg-McLane space K(π1(X), 1). Mathematics subject classification : 57R70; 55P15; 57Q10.

A simple language is defined, a probabilistic semantics and a partial correctness logic is proposed in terms of probabilistic relations. It is shown how a derandomized semantics can be constructed through the Eilenberg-Moore algebras. We investigate the category of EilenbergMoore algebras for the Giry monad associated with stochastic relations over Polish spaces with continuous maps as morphism...

Eilenberg machines define a general computational model. They are well suited to the simulation of problems specified using finite state formalisms such as formal languages and automata theory. This paper introduces a subclass of them called finite Eilenberg machines. We give a formal description of complete and efficient algorithms which permit the simulation of such machines. We show that our...

Let G be a finite group. For a based G-space X and a Mackey functor M , a topological Mackey functor X e ⊗M is constructed. When X is a based G-CW complex, X e ⊗M is shown to be an infinite loop space in the sense of G-spaces. This gives a version of the RO(G)-graded equivariant Dold-Thom theorem. Applying a variant of Elmendorf’s construction, we get a model for the Eilenberg-Mac Lane spectrum...

Let G denote an associative iï-space with unit (e.g. a topological group). We will show that the relations between G and a classifying space B Q axe more readily displayed using a geometric analog of the resolutions of homological algebra. The analogy is quite sharp, the stages of the resolution, whose base is BQ, determine a filtration of BQ. The resulting spectral sequence for cohomology is i...

The categorical formulation of the Eilenberg-Watts calculus relates, for any pair finite categories M and N, Fun^{le}(N,M) Fun^{re}(N,M) linear left or right exact functors Deligne product \bar N \boxtimes by adjoint equivalences. We establish a variant this case that are module over tensor category. This provides in particular canonical explicitly computable equivalences between (or, more gene...

We develop an algebraic underpinning of backtracking monad transformers in the general setting of monoidal categories. As our main technical device, we introduce Eilenberg–Moore monoids, which combine monoids with algebras for strong monads. We show that Eilenberg–Moore monoids coincide with algebras for the list monad transformer (‘done right’) known from Haskell libraries. From this, we obtai...

THE 3 ORIGINAL PAPERS ARE Paper I. Eilenberg T, Kronstrand L, Fink P, Frostholm L. Acceptance and commitment group therapy for health anxiety Results from a pilot study. J Anxiety Disord 2013 Jun 19;27(5):4618. Paper II. Eilenberg T., Fink P., Jensen JS, Rief W., Frostholm L. Acceptance and Commitment Group Therapy (ACT-G) for health anxiety: A randomised, controlled trial. Psychological Med 20...