Cohomological classification of Ann-functors
Nguyen Tien Quang, Dang Dinh Hanh
TL;DR
This paper extends the classification of Ann-functors by providing solutions using Mac Lane and Hochschild cohomology, generalizing previous work that used Shukla cohomology.
Contribution
It introduces a cohomological framework for classifying Ann-functors in the general case and for strong Ann-functors, utilizing Mac Lane and Hochschild cohomology.
Findings
Classification achieved via Mac Lane cohomology for general Ann-functors
Classification achieved via Hochschild cohomology for strong Ann-functors
Unified approach generalizes previous Shukla cohomology results
Abstract
Regular Ann-functor classification problem has been solved with Shukla cohomology. In this paper, we would like to present a solution to the above problem in the general case and in the case of strong Ann-functors with, respectively, Mac Lane cohomology and Hochschild cohomology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra