n-extension closed subcategories of $$(n+2)$$-angulated categories

Zhou, Panyue

doi:10.1007/s00013-022-01705-5

Cited by 3 publications

(1 citation statement)

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“…In the next example, we show how recent work of Klapproth [44] (see also [24,64]) produces examples of n-exangulated functors from an n-exact category into an ambient (n + 2)angulated category. This also gives more examples of n-exangulated subcategories.…”

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confidence: 97%

The category of extensions and a characterisation of $n$-exangulated functors

Bennett-Tennenhaus¹,

Haugland²,

Sandøy³

et al. 2022

Preprint

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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.

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confidence: 97%