Enriched Logical Connections

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F13%3A00206170" target="_blank" >RIV/68407700:21230/13:00206170 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10485-011-9267-y" target="_blank" >http://dx.doi.org/10.1007/s10485-011-9267-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-011-9267-y" target="_blank" >10.1007/s10485-011-9267-y</a>

Result language
angličtina
Original language name
Enriched Logical Connections
Original language description
Abstract: In the setting of enriched category theory, we describe dual adjunctions of the form Ldashv R:Spa^op --> Alg between the dual of the category Spa of ``spaces'' and the category Alg of ``algebras'' that arise from a schizophrenic object Omega, which is both an ``algebra'' and a ``space''. We call such adjunctions logical connections. We prove that the exact nature of Omega is that of a module that allows to lift optimally the structure of a ``space'' and an ``algebra'' to certain diagrams. Ourapproach allows to give a unified framework known from logical connections over the category of sets and analyzed, e.g., by Hans Porst and Walter Tholen, with future applications of logical connections in coalgebraic logic and elsewhere, where typically,both the category of ``spaces'' and the category of ``algebras'' consist of ``structured presheaves`'.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP202%2F11%2F1632" target="_blank" >GAP202/11/1632: Algebraic Methods in Proof Theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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