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David Nkansah

Publications and source records attributed to David Nkansah.

5 recordsLinked to original sources
arXiv2026

Codistinguished abelian subcategories

We introduce codistinguished abelian subcategories of triangulated categories, which generalise Jorgensen's proper abelian subcategories and are dual to Linckelmann's distinguished abelian subcategories. We show that they come equipped with a non-trivial exact structure induced by the ambient triangulated category, and that every exact structure on an abelian category arises in this way. We also show that fully faithful adjunction triples produce new codistinguished abelian subcategories from old.

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arXiv2025

Nakayama functors on proper abelian subcategories

We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that suitable proper abelian subcategories are dualising $k$-varieties and have enough projectives if and only if they have enough injectives. As an application, we provide a new proof of the existence of Auslander-Reiten sequences in the category of finite dimensional modules over a finite dimensional algebra.

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arXiv2025

Differential modules: a perspective on Bass' question

Guided by the $Q$-shaped derived category framework introduced by Holm and Jorgensen, we provide a differential module analogue of a classical result that characterises when a finitely generated module over a local commutative noetherian ring has finite injective dimension. As an application, we characterise local Cohen-Macaulay rings using the homological algebra of differential modules.

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arXiv2024

Rank functions on $(d+2)$-angulated categories -- a functorial approach

We introduce the notion of a rank function on a $(d+2)$-angulated category $\mathcal{C}$ which generalises the notion of a rank function on a triangulated category. Inspired by work of Chuang and Lazarev, for $d$ an odd positive integer, we prove that there is a bijective correspondence between rank functions defined on objects in $\mathcal{C}$ and rank functions defined on morphisms in $\mathcal{C}$. Inspired by work of Conde, Gorsky, Marks and Zvonareva, for $d$ an odd positive integer, we show there is a bijective correspondence between rank functions on $\operatorname{\mathsf{Proj}}A$ and additive functions on $\operatorname{\mathsf{mod}}(\operatorname{\mathsf{Proj}}A)$, where $\operatorname{\mathsf{Proj}}A$ is endowed with the Amiot-Lin $(d+2)$-angulated category structure. This allows us to show that every integral rank function on $\operatorname{\mathsf{Proj}}A$ can be decomposed into irreducible rank functions.

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