45 research outputs found
An -version of the Eilenberg-Moore theorem
No full textWe construct an -structure on the two-sided bar construction
involving homotopy Gerstenhaber algebras (hgas). It extends the non-associative
product defined by Carlson and the author and generalizes the dga structure on
the one-sided bar construction due to Kadeishvili-Saneblidze. As a consequence,
the multiplicative cohomology isomorphism from the Eilenberg-Moore theorem is
promoted to a quasi-isomorphism of -algebras.
We also show that the resulting product on the differential torsion product
involving cochain algebras agrees with the one defined by Eilenberg-Moore and
Smith, for all triples of spaces. This is a consequence of the following
result, which is of independent interest: The strongly homotopy commutative
(shc) structure on cochains inductively constructed by Gugenheim-Munkholm
agrees with the one previously defined by the author for all hgas.Comment: 31 page
Erratum and Addendum: Eilenberg-Moore algebras for stochastic relations
No full textAbstractIn Information and Computation 204 (2006), 1756–1781, the structure of Eilenberg-Moore algebras for the Giry monad for subprobabilities on Polish spaces is investigated in some detail by the present author. This note corrects a gap in one of the proofs. Additionally, it adapts the general results for the discrete Giry monad
Eilenberg-Moore categories and quiver representations of monads and comonads
No full textWe consider representations of quivers taking values in monads or comonads
over a Grothendieck category . We treat these as scheme like
objects whose ``structure sheaf'' consists of monads or comonads. By using
systems of adjoint functors between Eilenberg-Moore categories, we obtain a
categorical framework of modules over monad quivers, and of comodules over
comonad quivers. Our main objective is to give conditions for these to be
Grothendieck categories, which play the role of noncommutative spaces. As with
usual ringed spaces, we have to study two kinds of module categories over a
monad quiver. The first behaves like a sheaf of modules over a ringed space.
The second consists of modules that are cartesian, which resemble
quasi-coherent sheaves. We also obtain an extension of the classical
quasi-coherator construction to modules over a monad quiver with values in
Eilenberg-Moore categories. We establish similar results for comodules over a
comonad quiver. One of our key steps is finding a modulus like bound for an
endofunctor in terms of ,
where is a generator for and is a cardinal such
that is -presentable. Another feature of our paper is that we
study modules over a monad quiver in two different orientations, which we refer
to as ``cis-modules'' and ``trans-modules.'' We conclude with rational pairings
of a monad quiver with a comonad quiver, which relate comodules over a comonad
quiver to coreflective subcategories of modules over monad quivers.Comment: Paper much expanded in collaboration with additional author, from 15
pages to 35 page
Polynomial-Time Homology for Simplicial Eilenberg-MacLane Spaces
No full textIn an earlier paper of Čadek, Vokřínek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological spaces, under suitable restriction on the spaces. We aim at showing that, if the dimensions of the considered spaces are bounded by a constant, then the computations can be done in polynomial time. In this paper we make a significant technical step towards this goal: we show that the Eilenberg-MacLane space , represented as a simplicial group, can be equipped with polynomial-time homology (this is a polynomial-time version of effective homology considered in previous works of the third author and co-workers). To this end, we construct a suitable discrete vector field, in the sense of Forman's discrete Morse theory, on . The construction is purely combinatorial and it can be understood as a certain procedure for reducing finite sequences of integers, without any reference to topology. The Eilenberg-MacLane spaces are the basic building blocks in a Postnikov system, which is a "layered” representation of a topological space suitable for homotopy-theoretic computations. Employing the result of this paper together with other results on polynomial-time homology, in another paper we obtain, for every fixed k, a polynomial-time algorithm for computing the kth homotopy group π k (X) of a given simply connected space X, as well as the first k stages of a Postnikov system forX, and also a polynomial-time version of the algorithm of Čadek etal. mentioned abov
Institutional deviance in TV news: BBC, ITV and the Mid Staffordshire hospital scandal
No full textThis article is an empirical study of how institutional scandal is covered in TV news, using the BBC and ITV coverage of the Mid Staffordshire hospital scandal as a case study. It draws on sociology of deviance as well as Greer and McLaughlin’s model of institutional scandal and the different phases they go through. As such, the study examines how the coverage of the Mid Staffordshire hospital scandal moved through activations, reactions, amplification and accountability phases, although the progression was messy and complex. The study examines both verbal and visual elements of how TV news engaged in emotional accounts of suffering and attacks on figures of authority and public institutions. The article argues that institutional scandal and the media coverage of the NHS reflect both the politically disputed status of the NHS as well as a neoliberal drive to undermine public institutions.</jats:p
‘They need somebody to talk to':Parents' and carers' perceptions of school-based humanistic counselling
No full textAbstract Parents and carers are likely to take on a significant responsibility for managing an adolescent's mental health and well-being. Accordingly, their perceptions provide insight into the value of an intervention. This study explored parents' and carers' perceptions and expectations of school-based humanistic counselling, as received by a socially diverse group of young people (13–16 years old) in secondary schools in Greater London, UK. Semi-structured interviews from 17 parents and carers were analysed thematically. Two superordinate themes were identified: (a) the context of counselling, and (b) the content of counselling, the latter referring to stages of the therapeutic process and its outcomes. Schools were perceived as an ideal environment for the provision of professional mental health support, as it reaches young people in a natural, convenient setting and therefore promotes and/or widens access to universal support, as well as targeted interventions. Parents and carers further emphasised the importance of overall well-being, academic performance and social relationships.© 2021, The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See http://creativecommons.org/licenses/by/4.0/ <br/
Social choice and topology a case of pure and applied mathematics
No full textAbstractThe existence of a social choice model on a preference space P is a topological, even homotopical problem. It has been solved 50 years ago, under different terminology, by the author and, a little later, jointly with T. Ganea and P.J. Hilton. P must be an H-space and either contractible or homotopy equivalent to a product of Eilenberg-MacLane spaces over the rationals
Negotiating autonomy at the margins of the state:The dynamics of elite politics in the borderland of West Kalimantan, Indonesia
No full textRecent processes of decentralization have dramatically changed local political configurations and access to resources throughout Indonesia. In particular, the resource-rich regions at the margins of the state have, in the name of regional autonomy, experienced new spaces for manoeuvre in their claims for a larger share of forest resources. By stressing the unfolding relationship between local ethnic elites and the state, and their different strategies in negotiating and claiming authority over forests within Indonesia's changing forest regimes, the paper examines how local-level politics has taken on its special configuration in the remote border region of West Kalimantan, Indonesia. The author demonstrates this by focusing on the ongoing struggle over forest resources and by tracking the fate of a political movement for a new district in this resource-rich region. The paper further examines how current local elite strategies and networks can be related back to the period of border militarization in the 1960s and, once again, how these seem to challenge the exclusivity of the Indonesian-Malaysian border. The main argument is that central authority in the borderland has never been absolute, but waxes and wanes, and thus that state rules and laws are always up for local interpretation and negotiation, although the degree of such negotiation changes depending on the strength of the central state
