NDLI: Enriched Logical Connections

Content Provider	Springer Nature Link
Author	Kurz, Alexander Velebil, Jiří
Copyright Year	2011
Abstract	In the setting of enriched category theory, we describe dual adjunctions of the form $L\dashv R:{\mathsf{Spa}}^{op} \longrightarrow{\mathsf{Alg}}$ between the dual of the category Spa of “spaces” and the category Alg of “algebras” that arise from a schizophrenic object Ω, which is both an “algebra” and a “space”. We call such adjunctions logical connections. We prove that the exact nature of Ω is that of a module that allows to lift optimally the structure of a “space” and an “algebra” to certain diagrams. Our approach 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”.
Ending Page	377
Page Count	29
Starting Page	349
File Format	PDF
ISSN	09272852
e-ISSN	15729095
Journal	Applied Categorical Structures
Issue Number	4
Volume Number	21
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-09-23
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Schizophrenic object Geometry Convex and Discrete Geometry Logical connection Enriched categories (over closed or monoidal categories) Theory of Computation Special properties of functors (faithful, full, etc.) Module Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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