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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeOct 16th 2014
   • (edited Oct 16th 2014)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAt [[model structure on chain complexes ]], an 'anonymous editor' suggests that a line saying 'blah blah' should be completed to something more illuminating!

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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 17th 2014
   • (edited Oct 17th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexJust for reader's convenience: this refers to [this precise spot](http://ncatlab.org/nlab/show/model+structure+on+chain+complexes#fnref:1) in the entry.

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

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeOct 17th 2014
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItex(I just fixed a typo.)

   (I just fixed a typo.)

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 21st 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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](http://arxiv.org/abs/math.AT/0609537), [doi:10.1090/conm/436](http://dx.doi.org/10.1090/conm/436)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+chain+complexes/64">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+chain+complexes/64">v64</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+chain+complexes">current</a>

   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)

   diff, v64, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 21st 2020
   • (edited Aug 21st 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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](https://jdc.math.uwo.ca/summerschool/)_, University of Chicago, July 26-August 6, 2004, Chicago ([arXiv:math.AT/0604626](http://arxiv.org/abs/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](http://dx.doi.org/10.1090/conm/436)) * J.L. Castiglioni, G. Corti&#241;as, 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](http://arxiv.org/abs/math/0306289), [doi:10.1016/j.jpaa.2003.11.009](https://doi.org/10.1016/j.jpaa.2003.11.009)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+chain+complexes/64">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+chain+complexes/64">v64</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+chain+complexes">current</a>

   added references which claim (but don’t prove) the projective model structure on connective cochain complexes:

   The projective model structure on connective cochain 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)

   diff, v64, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 11th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexbriefly added the statement ([here](https://ncatlab.org/nlab/show/model+structure+on+chain+complexes#MonoidalModelStructureOnConnectiveChainComplexes)) that the projective model structure on connective chain complexes is monoidal. <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+chain+complexes/73">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+chain+complexes/73">v73</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+chain+complexes">current</a>

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

   diff, v73, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 20th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[William Dwyer]], [[Jan Spalinski]], Section 7 of: *[[Homotopy theories and model categories]]*, in: [[Ioan Mackenzie James|I. M. James]], *[[Handbook of Algebraic Topology]]*, North Holland 1995 ([ISBN:9780080532981](https://www.elsevier.com/books/handbook-of-algebraic-topology/james/978-0-444-81779-2), [doi:10.1016/B978-0-444-81779-2.X5000-7](https://doi.org/10.1016/B978-0-444-81779-2.X5000-7)) <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+chain+complexes/76">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+chain+complexes/76">v76</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+chain+complexes">current</a>

   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)

   diff, v76, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2021
   • (edited Jul 21st 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded ([here](https://ncatlab.org/nlab/show/model+structure+on+chain+complexes#PushoutAlongDegreewiseInjectionsPreservesQuasiIosmorphism)) statement and proof, following Prop. 24 in * [[Neil Strickland]], *The model structure for chain complexes* ([arXiv:2001.08955](https://arxiv.org/abs/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. <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+chain+complexes/77">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+chain+complexes/77">v77</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+chain+complexes">current</a>

   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.

   diff, v77, current