TL;DR
This paper introduces a weakened notion of S-categories, expanding on Kontsevich and Rosenberg's Q-categories, with examples and properties of (co)smooth objects within these categories.
Contribution
It proposes a new definition of S-categories by relaxing the axioms of Q-categories, providing foundational examples and exploring (co)smooth objects.
Findings
Examples of Q- and S-categories are provided.
Properties of (co)smooth objects are analyzed.
The new S-category framework broadens the scope of categorical structures.
Abstract
The definition of an S-category is proposed by weakening the axioms of a Q-category introduced by Kontsevich and Rosenberg. Examples of Q- and S-categories and (co)smooth objects in such categories are given.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology