Cauchy completeness for DG-categories

Branko Nikolić, Ross Street, Giacomo Tendas

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    1 Citation (Scopus)

    Abstract

    We go back to the roots of enriched category theory and study categories enriched in chain complexes; that is, we deal with differential graded categories (DG-categories for short). In particular, we recall weighted colimits and provide examples. We solve the 50 year old question of how to characterize Cauchy complete DG-categories in terms of existence of some specific finite absolute colimits. As well as the interac-tions between absolute weighted colimits, we also examine the total complex of a chain complex in a DG-category as a non-absolute weighted colimit.

    Original languageEnglish
    Pages (from-to)940-963
    Number of pages24
    JournalTheory and Applications of Categories
    Volume37
    Issue number28
    Publication statusPublished - 2021

    Keywords

    • chain complex
    • suspension
    • mapping cone
    • dierential graded algebra
    • Cauchy completion
    • DG-category
    • absolute colimit
    • total complex

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