Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

A note on a Holstein construction

Pages: 151 – 162

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a9


Sergey Arkhipov (Department of Mathematics, Aarhus University, Aarhus, Denmark)

Daria Poliakova (Department of Mathematics, Copenhagen University, Copenhagen, Denmark)


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.


DG category, model category, Reedy model structure

2010 Mathematics Subject Classification

18D20, 55U35

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