In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew category and we show that these constructions agree with the usual ones for algebras. In case of the smash product for an infinite group our construction specialized for a ring agrees with M. Beatti...

Internet marketplaces are now faced with new challenges that arise from the need to seamlessly integrate enormous number of product catalogs from different sources. In order to help users find products efficiently, Internet shops provide hierarchies of product catalogs (called category hierarchies). However, the absence of robust models (and well understood semantics) for product catalogs and t...

The notion of crossed product with a coquasi-Hopf algebra H is introduced and studied. The result of such a crossed product is an algebra in the monoidal category of right H-comodules. We give necessary and sufficient conditions for two crossed products to be equivalent. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed prod...

Links: [1] https://www.sbirttraining.com/node/1588 [2] http://www.rwjf.org/ [3] https://www.sbirttraining.com/category/product/tobacco [4] https://www.sbirttraining.com/category/tags/adolescents [5] https://www.sbirttraining.com/category/tags/motivational-interviewing [6] https://www.sbirttraining.com/category/resource-types/research-report [7] https://www.sbirttraining.com/category/topics/brie...

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S, S] . An idempotent e of this ring will split the homotopy category: [X,Y ] ∼= e[X,Y ]⊕(1−e)[X,Y ] . We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that i...

Links: [1] https://www.sbirttraining.com/node/1664 [2] http://www.jognn.org/article/S0884-2175(15)30320-8/pdf [3] https://www.sbirttraining.com/category/product/tobacco [4] https://www.sbirttraining.com/category/tags/cessation [5] https://www.sbirttraining.com/category/tags/prevention [6] https://www.sbirttraining.com/category/tags/women [7] https://www.sbirttraining.com/category/resource-types...

Everybody’s favorite theorem on Lusternik-Schnirelmann category is Eilenberg’s cup product theorem: if there is a nonzeroN-fold cup product in h̃∗(X), then cat(X) > N . Unfortunately, this theorem often fails to detect the full category of a space X; this is the case, for example, when X is a lens space Lp (with p odd) or X = Sp(n). In [4], Fadell and Husseini introduced the concept of the categ...

T research examines whether a low-ranking member in a high-status category (e.g., a low-end model of a high-end brand) or a high-ranking member in a low-status category (e.g., a high-end model of a low-end brand) is favored, holding the objective qualities of the items constant. Brand equity research suggests that the quality of a brand is more important than the ranking of a product within a b...