Spectra associated to symmetric monoidal bicategories

We show how to construct a Gamma-bicategory from a symmetric monoidal bicategory, and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way to relate this construction to the classic Gamma-category construction for a bipermutative category. As an example, we use this machinery to construct a delooping of the K-theory of a bimonoidal category as defined by Baas-Dundas-Rognes.Comment: 27 pages; originally submitted as: "An Infinite Loop Space Structure for K-theory of Bimonoidal Categories", this version has essentially the same content, but the organization is differen

Nerves and classifying spaces for bicategories

This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate `nerves of C' are homotopy equivalent. Any one of these realizations could therefore be taken as the classifying space BC of the bicategory. Its other major result proves a direct extension of Thomason's `Homotopy Colimit Theorem' to bicategories: When the homotopy colimit construction is carried out on a diagram of spaces obtained by applying the classifying space functor to a diagram of bicategories, the resulting space has the homotopy type of a certain bicategory, called the `Grothendieck construction on the diagram'. Our results provide coherence for all reasonable extensions to bicategories of Quillen's definition of the `classifying space' of a category as the geometric realization of the category's Grothendieck nerve, and they are applied to monoidal (tensor) categories through the elemental `delooping' construction.Comment: 42 page

The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss generalised mapping properties of these theories, and relations of these properties to corings. Using this, we give conditions for the Serre spectral sequence to hold for a noncommutative fibration. This might be better read as giving the definition of a fibration in noncommutative differential geometry. We also study the multiplicative structure of such spectral sequences. Finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration, and in the process clarify the differential structure on these homogeneous spaces. We also give two explicit examples of differential fibrations: these are built on the quantum Hopf fibration with two different differential structures.Comment: LaTeX, 33 page

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Quantum Picturalism

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper conceptual understanding of quantum theory, as well as its unification with other physical theories. Specific applications discussed here are purely diagrammatic proofs of several quantum computational schemes, as well as an analysis of the structural origin of quantum non-locality. The underlying mathematical foundation of this high-level diagrammatic formalism relies on so-called monoidal categories, a product of a fairly recent development in mathematics. These monoidal categories do not only provide a natural foundation for physical theories, but also for proof theory, logic, programming languages, biology, cooking, ... The challenge is to discover the necessary additional pieces of structure that allow us to predict genuine quantum phenomena.Comment: Commissioned paper for Contemporary Physics, 31 pages, 84 pictures, some colo

The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Electromyographic Activity of Hand Muscles in a Motor Coordination Game: Effect of Incentive Scheme and Its Relation with Social Capital

Background. A vast body of social and cognitive psychology studies in humans reports evidence that external rewards, typically monetary ones, undermine intrinsic motivation. These findings challenge the standard selfish-rationality assumption at the core of economic reasoning. In the present work we aimed at investigating whether the different modulation of a given monetary reward automatically and unconsciously affects effort and performance of participants involved in a game devoid of visual and verbal interaction and without any perspective-taking activity. Methodology/Principal Findings Twelve pairs of participants were submitted to a simple motor coordination game while recording the electromyographic activity of First Dorsal Interosseus (FDI), the muscle mainly involved in the task. EMG data show a clear effect of alternative rewards strategies on subjects' motor behavior. Moreover, participants' stock of relevant past social experiences, measured by a specifically designed questionnaire, was significantly correlated with EMG activity, showing that only low social capital subjects responded to monetary incentives consistently with a standard rationality prediction. Conclusions/Significance Our findings show that the effect of extrinsic motivations on performance may arise outside social contexts involving complex cognitive processes due to conscious perspective-taking activity. More importantly, the peculiar performance of low social capital individuals, in agreement with standard economic reasoning, adds to the knowledge of the circumstances that makes the crowding out/in of intrinsic motivation likely to occur. This may help in improving the prediction and accuracy of economic models and reconcile this puzzling effect of external incentives with economic theory

Peer norm guesses and self-reported attitudes towards performance-related pay

Due to a variety of reasons, people see themselves differently from how they see others. This basic asymmetry has broad consequences. It leads people to judge themselves and their own behavior differently from how they judge others and others’ behavior. This research, first, studies the perceptions and attitudes of Greek Public Sector employees towards the introduction of Performance-Related Pay (PRP) systems trying to reveal whether there is a divergence between individual attitudes and guesses on peers’ attitudes. Secondly, it is investigated whether divergence between own self-reported and peer norm guesses could mediate the acceptance of the aforementioned implementation once job status has been controlled for. This study uses a unique questionnaire of 520 observations which was designed to address the questions outlined in the preceding lines. Our econometric results indicate that workers have heterogeneous attitudes and hold heterogeneous beliefs on others’ expectations regarding a successful implementation of PRP. Specifically, individual perceptions are less skeptical towards PRP than are beliefs on others’ attitudes. Additionally, we found that managers are significantly more optimistic than lower rank employees regarding the expected success of PRP systems in their jobs. However, they both expect their peers to be more negative than they themselves are