City Research Online

Abstract

Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of extensions, which encodes important structural information. We study how functors between categories of extensions relate to those at the level of the original categories. When the additive categories in question are n-exangulated, this leads to a characterisation of n-exangulated functors. Our approach enables us to study n-exangulated categories from a 2-categorical perspective. We introduce n-exangulated natural transformations and characterise them using categories of extensions. Our characterisations allow us to establish a 2-functor between the 2-categories of small n-exangulated categories and small exact categories. A similar result with no smallness assumption is also proved. We employ our theory to produce various examples of n-exangulated functors and natural transformations. Although the motivation for this article stems from representation theory and the study of n-exangulated categories, our results are widely applicable: several require only an additive category equipped with a biadditive functor with no extra assumptions; others can be applied by endowing an additive category with its split n-exangulated structure.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00209-023-03341-3
Publisher Keywords:	Additive category, Biadditive functor, Category of extensions, Extriangulated category, Extriangulated functor, n-Exangulated category, n-Exangulated functor, 2-Category, 2-Functor
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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