Algebras with actions and automata

Kühnel, Wolfgang; Pfender, Michael; Meseguer, José; Sols, Ignacio

doi:10.1155/s0161171282000076

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…For ungraded algebra objects in Set, these results can be found in any good introduction to the subject, for example [Ber98]. The more general cases can be found in the wider literature, for example in [KPMS82]. We record these results here, mostly without proofs, to establish notation and as a quick reference for the rest of the paper.…”

Section: General Algebramentioning

confidence: 93%

Tall-Wraith Monoids

Stacey¹,

Whitehouse²

2011

Preprint

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Tall-Wraith monoids were introduced in [SW09] to describe the algebraic structure on the set of unstable operations of a suitable generalised cohomology theory. In this paper we begin the study of Tall-Wraith monoids in an algebraic and categorical setting. We show that for V a variety of algebras, applying the free V-algebra functor to a monoid in Set produces a Tall-Wraith monoid. We also study the example of the Tall-Wraith monoid defined by the self set-maps of a finite ring, an example closely related to the original motivation for Tall-Wraith monoids. * The authors acknowledge the support of the EPSRC, grant no.: GR/S76823 /01.

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Section: General Algebramentioning

confidence: 93%

Tall-Wraith Monoids

Stacey¹,

Whitehouse²

2011

Preprint

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show abstract

“…For ungraded algebra objects in Set, these results can be found in any good introduction to the subject, for example in [Ber98]. The more general cases can be found in the wider literature, for example in [KPMS82]. We record these results here without proofs to establish notation and as a quick reference for the rest of the paper.…”

Section: General Algebramentioning

confidence: 93%

The hunting of the Hopf ring

Stacey¹,

Whitehouse

2009

Homology, Homotopy and Applications

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We provide a new algebraic description of the structure on the set of all unstable cohomology operations for a suitable generalised cohomology theory, E * (−). Our description is as a graded and completed version of a Tall-Wraith monoid. The E * -cohomology of a space X is a module for this Tall-Wraith monoid. We also show that the corresponding Hopf ring of unstable co-operations is a module for the Tall-Wraith monoid of unstable operations. Further examples are provided by considering operations from one theory to another.

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Algebras with actions and automata

Abstract: ABSTRACT.In the present paper we want to give a common structure The particular case of algebras with fixed "natural numbers object" has been studied by the authors in [23].

Cited by 2 publications

References 3 publications

Tall-Wraith Monoids

Tall-Wraith Monoids

The hunting of the Hopf ring

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