1. Introduction Given any graded commutative ring R with identity, a Hopf ring over R is a com-mutative ring in the category of graded R-coalgebras. Such objects arise naturally in algebraic topology, as explained below, and their investigation was pioneered by Ravenel and Wilson in 14]. To any spectrum G we may associate an-spectrum fG r : r 2 Zg by choosing G r to be the space representing th...

We prove a categorification of the stable elements formula Cartan and Eilenberg. Our expresses derived category module group as bilimit corresponding categories for p-subgroups.

Eilenberg machines have been introduced in 1974 in the field of formal language theory. They are finite automata for which the alphabet is interpreted by mathematical relations over an abstract set. They generalize many finite state machines. We consider in the present work the subclass of finite Eilenberg machines for which we provide an executable complete simulator. This program is specified...

We use the homological perturbation lemma to give an explicit proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.

1. The telescope conjecture and Bousfield localization 4 1.1. Telescopes 4 1.2. Bousfield localization and Bousfield classes 6 1.3. The telescope conjecture 8 1.4. Some other open questions 9 2. Some variants of the Adams spectral sequence 10 2.1. The classical Adams spectral sequence 11 2.2. The Adams-Novikov spectral sequence 12 2.3. The localized Adams spectral sequence 15 2.4. The Thomified...

With Fq a finite field of characteristic p, let F(q) be the category whose objects are functors from finite dimensional Fq–vector spaces to F̄p– vector spaces. Extension groups in F(q) can be interpreted as MacLane (or Topological Hochschild) cohomology with twisted coefficients. Furthermore, evaluation on an m dimensional vector space Vm induces a homorphism from Ext F(q) (F, G) to finite group...