Local theory of almost split sequences for comodules

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Abstract

We show that almost split sequences in the category of comodules over a coalgebra Γ 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.

Original languageEnglish (US)
Pages (from-to)183-196
Number of pages14
JournalAnnali dell'Universita di Ferrara
Volume51
Issue number1
DOIs
StatePublished - 2005

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ASJC Scopus subject areas

  • Mathematics(all)

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