Sergio Pavon
Published 2023-12-07Version 1
We introduce the notion of torsion-simple objects in an abelian category: these are the objects which are always either torsion or torsion-free with respect to any torsion pair. We present some general results concerning their properties, and then proceed to investigate the notion in various contexts, such as the category of modules over an artin algebra or a commutative noetherian ring, and the category of quasi-coherent sheaves over the projective line.
Comments: 17 pages. Comments are welcome
The heart fan of an abelian category
Representation of n-abelian categories in abelian categories
The long $n$-exact sequence theorem in $n$-abelian categories
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