Added (here) statement and proof, following Prop. 24 in

- Neil Strickland,
*The model structure for chain complexes*(arXiv:2001.08955)

(which I added), that the model structures with (co)fibrations the degreewise injections/surjections are proper.

No proof yet that this works for bounded chain complexes with conditions in positive degrees.

]]>added pointer to:

- William Dwyer, Jan Spalinski, Section 7 of:
*Homotopy theories and model categories*, in: I. M. James,*Handbook of Algebraic Topology*, North Holland 1995 (ISBN:9780080532981, doi:10.1016/B978-0-444-81779-2.X5000-7)

briefly added the statement (here) that the projective model structure on connective chain complexes is monoidal.

]]>added references which claim (but don’t prove) the projective model structure on connective *co*chain complexes:

The projective model structure on connective *co*chain complexes is claimed, without proof, in:

Kathryn Hess, p. 6 of

*Rational homotopy theory: a brief introduction*, contribution to*Summer School on Interactions between Homotopy Theory and Algebra*, University of Chicago, July 26-August 6, 2004, Chicago (arXiv:math.AT/0604626), chapter in Luchezar Lavramov, Dan Christensen, William Dwyer, Michael Mandell, Brooke Shipley (eds.),*Interactions between Homotopy Theory and Algebra*, Contemporary Mathematics 436, AMS 2007 (doi:10.1090/conm/436)J.L. Castiglioni, G. Cortiñas, Def. 4.7 of:

*Cosimplicial versus DG-rings: a version of the Dold-Kan correspondence*, J. Pure Appl. Algebra 191 (2004), no. 1-2, 119–142, (arXiv:math.KT/0306289, doi:10.1016/j.jpaa.2003.11.009)

added pointer to

- Paul Goerss, Kirsten Schemmerhorn, Theorem 1.5 in:
*Model categories and simplicial methods*, Notes from lectures given at the University of Chicago, August 2004, in:*Interactions between Homotopy Theory and Algebra*, Contemporary Mathematics 436, AMS 2007(arXiv:math.AT/0609537, doi:10.1090/conm/436)

(I just fixed a typo.)

]]>Just for reader’s convenience: this refers to this precise spot in the entry.

]]>At model structure on chain complexes, an ’anonymous editor’ suggests that a line saying ’blah blah’ should be completed to something more illuminating!

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