Concrete Duality for Strict Infinity Categories
G.V. Kondratiev
TL;DR
This paper develops a foundational theory of strict infinity categories and explores their role in concrete dualities, providing new examples and criteria for their existence.
Contribution
It introduces an elementary framework for strict infinity categories and formulates a criterion for natural dualities in higher categories, with new examples.
Findings
Established a theory of strict infinity categories
Formulated a criterion for the existence of natural dualities in higher categories
Presented new examples of concrete dualities
Abstract
An elementary theory of strict -categories with application to concrete duality is given. All known famous dualities (Gelfand-Naimark, Pontryagin, Stone, etc.) are so-called natural. A criterion of existence of such a duality for higher categories is formulated. New examples are presented.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Rings, Modules, and Algebras