A note on a Holstein construction

We clarify details and fill certain gaps in the construction of a canonical Reedy fibrant resolution for a constant simplicial DG-category due to Holstein.

Keywords

DG category, model category, Reedy model structure

2010 Mathematics Subject Classification

18D20, 55U35

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The first author was partially supported by QGM. The second author was partially supported by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. N 14.641.31.0001. The second author was also supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).

Note added by authors: Despite what we wrote on page 2 of this article, the proof of Proposition 3.3 in [Tab2] did not contain any mathematical inaccuracies or flaws. Rather, it was a question of exposition: a trivial computation was omitted without explicitly mentioning the fact, and this led the author of [Hol] to wrong conclusions. The proof in [Hol] thus indeed contains a gap that is fixed in this article.

Received 5 February 2019

Accepted 28 June 2019

Published 15 April 2020