scholarly journals A category equivalence for odd Sugihara monoids and its applications

2012 ◽  
Vol 216 (10) ◽  
pp. 2177-2192 ◽  
Author(s):  
N. Galatos ◽  
J.G. Raftery
Keyword(s):  
Category Equivalence

Constraints on Code-Switching: Evidence from Swedish and English

1986 ◽  
Vol 9 (1) ◽  
pp. 55-82
Author(s):  
Beata Schmid
Keyword(s):  
Code Switching ◽  
Optimal Switching ◽  
Specific Point ◽  
Clear Cut ◽  
Clear Sense ◽  
Closed Class ◽  
The Matrix ◽  
Category Equivalence ◽  
Communicative Context

In this paper, I have shown that Joshi's (1982) framework of codeswitching constraints can largely be applied to Swedish-English code-switches. I feel qualified to conclude that Joshi's claims concerning the non-switchability of closed class items and matrix language and embedded languages are held up by the Swedish- English data. The need for corresponding categories proved to be less clear-cut than originally proposed by Woolford (1983) and others. It seems that optimal switching conditions are given if the categories, rules and metarules correspond in the two languages. Apparently, however, it is also possible to switch if the node admissibility conditions for the matrix language only are met, as was shown by code-switched sentences containing RPs. This requires that the speaker has a clear sense of which language is the host and which is embedded. Rules from the embedded language only are not acceptable. This calls for some sort of determination strategy by the parser. I found no evidence for determining Lm at any specific point in the sentence, except at the topmost S. Rather, the judgments by code-switchers that a sentence “comes from” one language seems to coincide with the fact that the resulting sentence is based on the rules from that language. Other than that, the matrix language is determined by the communicative context as a whole.The data involving RPs also seemed to indicate that RPs are not separate ategories, but are NPs, introduced by a “de-slashing” rule (Sells 1984). If they were separate categories, this would be evidence for there being no need for category equivalence. In this case, we would have to explicitly state all other cases which require category equivalence (the majority of cases), which is undesirable.

On Morita Duality

1969 ◽  
Vol 21 ◽  
pp. 1338-1347 ◽  
Author(s):  
Bruno J. Mùller
Keyword(s):  
Direct Sums ◽  
Category Equivalence ◽  
Reflexive Modules

A contra variant category-equivalence between categories of right R-modules and left S-modules (all rings have units, all modules are unitary) that contain RR, SS and are closed under submodules and factor modules, is naturally equivalent to a functor Horn (–, U) with a bimodule SUR such that SU, UR are injective cogenerators with S = End UR and R = End SU, and all modules in are [U-reflexive. Conversely, for any SSUR, Hom(–, U) is a contravariant category equivalence between the categories of [U-reflexive modules, and if U has the properties just stated, then these categories are closed under submodules, factor modules, and finite direct sums and contain RR, UR,SS, and SU. Such a functor will be called a (Morita) duality between R and S induced by U (see (5)).

Hopf Quasimodules and Yetter-Drinfeld Modules over Hopf Quasigroups

2021 ◽  
Vol 28 (02) ◽  
pp. 213-242
Author(s):  
Tao Zhang ◽  
Yue Gu ◽  
Shuanhong Wang
Keyword(s):  
Monoidal Category ◽  
Drinfeld Modules ◽  
Braided Monoidal Category ◽  
Symmetric Monoidal Category ◽  
Category Equivalence ◽  
Hopf Modules ◽  
Hopf Quasigroup

We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup [Formula: see text] in a symmetric monoidal category [Formula: see text]. If [Formula: see text] possesses an adjoint quasiaction, we show that symmetric Yetter-Drinfeld categories are trivial, and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over [Formula: see text] and the category of four-angle Hopf modules over [Formula: see text] under some suitable conditions.

scholarly journals A note on the Matlis category equivalence

2006 ◽  
Vol 299 (2) ◽  
pp. 854-862 ◽  
Author(s):  
Sang Bum Lee
Keyword(s):  
Category Equivalence

scholarly journals Homotopy theory of Moore flows (II)

2021 ◽  
Vol 36 (2) ◽  
pp. 157-239
Author(s):  
Philippe Gaucher
Keyword(s):  
Internal Structure ◽  
Homotopy Theory ◽  
Left Adjoint ◽  
Main Step ◽  
Derived Functor ◽  
Category Equivalence ◽  
Q Model ◽  
Quillen Equivalent ◽  
Model Structures

This paper proves that the q-model structures of Moore flows and of multipointed d-spaces are Quillen equivalent. The main step is the proof that the counit and unit maps of the Quillen adjunction are isomorphisms on the q-cofibrant objects (all objects are q-fibrant). As an application, we provide a new proof of the fact that the categorization functor from multipointed d-spaces to flows has a total left derived functor which induces a category equivalence between the homotopy categories. The new proof sheds light on the internal structure of the categorization functor which is neither a left adjoint nor a right adjoint. It is even possible to write an inverse up to homotopy of this functor using Moore flows.

Adjoints and Category Equivalence

2009 ◽  
pp. 131-138
Author(s):  
Robert R. Colby ◽  
Kent R. Fuller
Keyword(s):  
Category Equivalence

scholarly journals A LOGICAL AND ALGEBRAIC CHARACTERIZATION OF ADJUNCTIONS BETWEEN GENERALIZED QUASI-VARIETIES

2018 ◽  
Vol 83 (3) ◽  
pp. 899-919 ◽  
Author(s):  
TOMMASO MORASCHINI
Keyword(s):  
Algebraic Characterization ◽  
Adjoint Functors ◽  
Algebraic Description ◽  
Category Equivalence

AbstractWe present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the concept of adjunction and a new notion of translation between relative equational consequences.

scholarly journals Topological realizations and fundamental groups of higher-rank graphs

2015 ◽  
Vol 59 (1) ◽  
pp. 143-168 ◽  
Author(s):  
S. Kaliszewski ◽  
Alex Kumjian ◽  
John Quigg ◽  
Aidan Sims
Keyword(s):  
Fundamental Group ◽  
Abelian Groups ◽  
Fundamental Groups ◽  
Crossed Products ◽  
Finitely Generated ◽  
Topological Realization ◽  
Category Equivalence ◽  
Free Abelian Groups ◽  
Higher Rank ◽  
Projective Limits

AbstractWe investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization. We also show that topological realization of higher-rank graphs is a functor and that for each higher-rank graphΛ, this functor determines a category equivalence between the category of coverings ofΛand the category of coverings of its topological realization. We discuss how topological realization relates to two standard constructions fork-graphs: projective limits and crossed products by finitely generated free abelian groups.

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