The most familiar example of higher, or vertically iterated enrichment is that in the definition of strict n-category. We begin with strict n-categories based on a general symmetric monoidal category V. Motivation is offered through a comparison of the classical and extended versions of topological quantum field theory. A sequence of categorical types that filter the category of monoidal catego...

Modern retailers typically manage thousands of individual stock keeping units (skus) and are faced with the complex task of stocking, pricing, promoting and maintaining an appropriate product assortment. This task is further complicated by the substantial heterogeneity in consumer preference for di®erent product o®erings. In this environment, it is critical that retail management has some under...

(1) A Frobenius algebra in a tensor category C is an abstract algebracoalgebra where (co)multiplication and (co)unit are arrows in C. A Frobenius extension A|S may be viewed as a Frobenius algebra in the category M of S-bimodules under ordinary tensor product over S, as described in connection with corings in NEFE, chapter 4. The notion of a special Frobenius algebra in a category is a basic no...

We develop a spreading activation model, which we call the category activation model, to predict where within a category structure consumers are likely to position a subcategory that they have created to accommodate a new hybrid product. Based on this model, we hypothesize that the probability that an individual will position a new category subordinate to a particular category i is proportional...

We introduce Yetter-Drinfeld modules over a weak Hopf algebra H, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of H-modules. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak DoiHopf modules, and, a fortiori, a...

The theory of crystal bases introduced by Kashiwara in [6] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [7] he define...

The complexity of managing a category assortment has grown tremendously in recent years due to the increased product turn-over and proliferation rates in most categories. It is an increasingly di±cult task for managers to ̄nd an e®ective assortment due to uncertain consumer preferences and the exponential number of possible assortments. This paper presents an empirically-based modeling framewor...

The theory of crystal bases introduced by Kashiwara in [4] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [5] he define...

Although price promotions have increased in both commercial use and quantity of academic research over the last decade, most of the attention has been focused on their effects on brand choice and brand sales. By contrast, little is known about the conditions under which price promotions expand short-run and long-run category demand, even though the benefits of category expansion can be substant...

industrial design is attempting to answer physical, emotional and functional needs of human by including different fields such as product design, transporting design, interaction design and etc. products have various functions and appearances, due to their users’ specifications. industrial design is attempting to answer physical, emotional and functional needs of human by including different fi...