Resolution Dimension Relative to Resolving Subcategories in Extriangulated Categories

Tan, Lingling; Liu, Li

doi:10.3390/math9090980

Cited by 3 publications

(1 citation statement)

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“…2.6], we let δ ⊕ ρ ∈ E(C ⊕ D, A ⊕ B) denote the element corresponding to (δ, 0, 0, ρ) via this isomorphism. It is straightforward to check that this gives a biproduct of extensions making E -Ext(C) an additive category; see, for instance, Liu-Tan [60,Rem. 2].…”

Section: The Category Of Extensions and N-exangulated Functorsmentioning

confidence: 99%

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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Section: The Category Of Extensions and N-exangulated Functorsmentioning

confidence: 99%