Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On adjoint functors of the Heller operator   Given an abelian category A with enough projectives, we can form its stable
category _A_ := A/Proj(A)$. The Heller operator Omega : _A_ -> _A_ is
characterised on an object X by a choice of a short exact sequence Omega X -> P
-> X in A with P projective. If A is Frobenius, then Omega is an equivalence,
hence has a left and a right adjoint. If A is hereditary, then Omega is zero,
hence has a left and a right adjoint. In general, Omega is neither an
equivalence nor zero. In the examples we have calculated via Magma, it has a
left adjoint, but in general not a right adjoint. If A has projective covers,
then Omega preserves monomorphisms; this would also follow from Omega having a
left adjoint. I do not know an example where Omega does not have a left
adjoint.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph