scholarly journals Distributive laws for Lawvere theories

2020 ◽  
Vol 2 ◽  
pp. 1 ◽  
Author(s):  
Eugenia Cheng

Distributive laws give a way of combining two algebraic structures expressed as monads; in this paper we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches, involving profunctors, monoidal profunctors, an extension of the free finite-product category 2-monad from Cat to Prof, and factorisation systems respectively. We exhibit comparison functors between CAT and each of these new frameworks to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The different but equivalent formulations then provide, between them, a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws.

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Stefano Marseglia

Abstract In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties A isogenous to $$B^r$$Br, where the characteristic polynomial g of Frobenius of B is an ordinary square-free q-Weil polynomial, for a power q of a prime p, or a square-free p-Weil polynomial with no real roots. Under some extra assumptions on the polynomial g we give an explicit description of all the isomorphism classes which can be computed in terms of fractional ideals of an order in a finite product of number fields. In the ordinary case, we also give a module-theoretic description of the polarizations of A.


2018 ◽  
Vol 27 (1) ◽  
Author(s):  
Annette Evans

In this article descriptions of angelic movement in the Twelfth Song are compared to descriptions of such activity arising from the throne of God in Ezekiel’s vision in Ezekiel 1 and 10, and to that in the Seventh Song as contained in scroll 4Q403. The penultimate Twelfth Song of the Songs of the Sabbath Sacrifice culminates in a more explicit description of angelic messenger activity and in other nuances. The Twelfth Song was intended to be read on the Sabbath immediately following Shavu’ot, when the traditional synagogue reading is Ezekiel 1 and Exodus 19–20. The possible significance for the author of Songs of the Sabbath Sacrifice of the connection between the giving of the Law at Mount Sinai and Ezekiel’s vision where merkebah thrones and seats appear in the plural form is considered in the conclusion


2014 ◽  
Vol 4 (2) ◽  
Author(s):  
Prof. Amit Shrivastava ◽  
Prof. Sushil Kumar Pare ◽  
Prof (Dr) Saumya Singh

Inadequate is the empirical research on store choice model in view of retail store attributes with endogenous construct of store patronage intention of consumer. Conventional wisdom and social science research-based insights for underpinning the design of store environment established elements such as music, scent, crowding and physical attractiveness of the store. Earlier empirical findings lack on key anterior, which include consumers’ time and effort as well as the psychological costs such as convenient, economical, risk mitigated shopping experience. The premise on which overall effects in our model rests, is that store attributes influence consumers' cognitive process and develop perceptual framework of store choice criteria — namely, convenience, reputation of outlet, branded merchandise (mediated through perceived quality). This research presents a formal test of the linear regression equation model in the context of store choice behaviour, involving one product category. The present paper explores these attributes and their affect on consumer from different socio-economic classes, willingness to purchase and to patronize if these factors are modified. Questioning the earlier conclusions that all attributes aforementioned are equally important in consumer decision making, the current results indicate that consumers place differential significance on each attribute, and the level of significance placed on each attribute varies with different socio economic class. These findings are significantly important to the retail industry as they identify the critical attributes responsible for building consumer choice and patronage among different socio economy classes. This model also paves way for another premise of empirical research, that shoppers might develop category-wise store choice or patronage behaviour model.


2021 ◽  
pp. 000183922110123
Author(s):  
Johnny Boghossian ◽  
Robert J. David

Categories are organized vertically, with product categories nested under larger umbrella categories. Meaning flows from umbrella categories to the categories beneath them, such that the construction of a new umbrella category can significantly reshape the categorical landscape. This paper explores the construction of a new umbrella category and the nesting beneath it of a product category. Specifically, we study the construction of the Quebec terroir products umbrella category and the nesting of the Quebec artisanal cheese product category under this umbrella. Our analysis shows that the construction of umbrella categories can unfold entirely separately from that of product categories and can follow a distinct categorization process. Whereas the construction of product categories may be led by entrepreneurs who make salient distinctive product attributes, the construction of umbrella categories may be led by “macro actors” removed from the market. We found that these macro actors followed a goal-derived categorization process: they first defined abstract goals and ideals for the umbrella category and only subsequently sought to populate it with product categories. Among the macro actors involved, the state played a central role in defining the meaning of the Quebec terroir category and mobilizing other macro actors into the collective project, a finding that suggests an expanded role of the state in category construction. We also found that market intermediaries are important in the nesting of product categories beneath new umbrella categories, notably by projecting identities onto producers consistent with the goals of the umbrella category. We draw on these findings to develop a process model of umbrella category construction and product category nesting.


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