On abelian 2-categories and derived 2-functors
Teimuraz Pirashvili
TL;DR
This paper explores abelian 2-categories, introduces derived 2-functors, and proves key theorems like Gabriel-Mitchel and Morita theory for 2-rings, advancing the understanding of higher categorical algebra.
Contribution
It introduces derived 2-functors and proves foundational theorems such as Gabriel-Mitchel and Morita theory in the context of 2-categories, extending classical results to higher categories.
Findings
Derived 2-functors are developed and analyzed.
Proof of Gabriel-Mitchel theorem for 2-categories.
Morita theory for 2-rings established.
Abstract
This is an extended version of my earlier articel "Projective and injective objects in symmetric categorical groups. arXiv:1007.0121v1." Several new facts added, including the material on the derived 2-functors and the proof of the Gabriel-Mitchel theorem and the Morita theory for 2-rings.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models