On monads and warpings

We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a generalization of monoidal categories in which the associativity and unit maps are not required to be invertible. Our analysis leads us to describe a normalization process for skew monoidal categories, which produces a universal skew monoidal category for which the right unit map is invertible.Comment: 15 pages. Version 2: revised based on a very helpful report from the referee. To appear in the Cahiers de Topologie and Geometrie Differentielle Categorique

A skew-duoidal Eckmann-Hilton argument and quantum categories

A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory M. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in M. Now we see in what kind of M quantum categories are merely monads.Comment: 14 pages, dedicated to George Janelidze on the occasion of his 60th birthday; v2 final version, 15 pages, to appear in Applied Categorical Structure

Triangulations, orientals, and skew monoidal categories

A concrete model of the free skew-monoidal category Fsk on a single generating object is obtained. The situation is clubbable in the sense of G.M. Kelly, so this allows a description of the free skew-monoidal category on any category. As the objects of Fsk are meaningfully bracketed words in the skew unit I and the generating object X, it is necessary to examine bracketings and to find the appropriate kinds of morphisms between them. This leads us to relationships between triangulations of polygons, the Tamari lattice, left and right bracketing functions, and the orientals. A consequence of our description of Fsk is a coherence theorem asserting the existence of a strictly structure-preserving faithful functor from Fsk to the skew-monoidal category of finite non-empty ordinals and first-element-and-order-preserving functions. This in turn provides a complete solution to the word problem for skew monoidal categories.Comment: 48 page

Forensic Finance: Enron and Others

In finance, as in pathology, we can learn more from failure than from success. This lecture examines three famous financial failures, Metallgesellschaft’s oil futures business, LTCM and related hedge fund failures, and the current travails of ENRON, and performs a post mortem on each to see what can be learned. Not surprisingly, the cause of death was similar in each case, or, to put it more familiarly, history always repeats itself.

Wage Premia in Employment Clusters: How Important is Worker Heterogeneity?

This paper tests whether the correlation between wages and the spatial concentration of employment can be explained by unobserved worker productivity differences. Residential location is used as a proxy for a worker's unobserved productivity, and average workplace commute time is used to test whether location-based productivity differences are compensated away by longer commutes. Analyses using confidential data from the 2000 Decennial Census Long Form find that the agglomeration estimates are robust to comparisons within residential location and that the estimates do not persist after controlling for commuting costs suggesting that the productivity differences across locations are not due to productivity differences across individuals.Agglomeration, Wages, Sorting, Locational Equilibrium, Human Capital Externalities