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arXiv · 2107.11086

Remarks on partially abelian exact categories

Theo Buehler
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Abstract

The purpose of this short and elementary note is to identify some classes of exact categories introduced in L. Previdi's thesis. Among other things we show: (1) An exact category is partially abelian exact if and only if it is abelian. (2) An exact category satisfies the axioms AIC and AIC° if and only if it is quasi-abelian in the sense of J.-P. Schneiders. (3) An exact category satisfies AIC if and only if it is an additive category of the type considered by G. Laumon in his work on derived categories of filtered ${\cal D}$-modules. In all of the above classes all morphisms have kernels and coimages and the exact structure must be given by all kernel-cokernel pairs.

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Theo Buehler. 2021-10-03. Remarks on partially abelian exact categories. https://arxiv.org/abs/2107.11086

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