Local theory of almost split sequences for comodules

Details Local theory of almost split sequences for comodules Local theory of almost split sequences for comodules

2005-04-05

arxiv.org/abs/math/0504081v1

Mathematics

Representation Theory

Scientific paper

We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that such almost split sequences exist if the right hand term has a quasifinitely copresented linear dual. Conversely, taking limits of almost split sequences over finte-dimensional comodule categories, we then show that, for countable-dimensional coalgebras, certain exact sequences exist which satisfy a condition weaker than being almost split, which we call ``finitely almost split''. Under additional assumptions, these sequences are shown to be almost split in the appropriate category.

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