Geodesic
Cauchy completeness for DG-categories
Theory and applications of categories, Tome 37 (2021), pp. 940-963 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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 interactions between absolute weighted colimits, we also examine the total complex of a chain complex in a DG-category as a non-absolute weighted colimit.

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Classification : 18D20, 18G35, 18E30, 55P42
Keywords: chain complex, suspension, mapping cone, differential graded algebra, Cauchy completion, DG-category, absolute colimit, total complex 
@article{TAC_2021_37_a27,
     author = {Branko Nikoli\'c and Ross Street and Giacomo Tendas},
     title = {Cauchy completeness for {DG-categories}},
     journal = {Theory and applications of categories},
     pages = {940--963},
     year = {2021},
     volume = {37},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a27/}
}
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Branko Nikolić; Ross Street; Giacomo Tendas. Cauchy completeness for DG-categories. Theory and applications of categories, Tome 37 (2021), pp. 940-963. http://geodesic.mathdoc.fr/item/TAC_2021_37_a27/