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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 27th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to [[injective object]] propositions and examples for injective modules and injective abelian groups P.S. I am checking if I am missing something: To&euml;n on <a href="http://arxiv.org/PS_cache/math/pdf/0012/0012219v6.pdf#page=48">page 48/49 here</a> behaves as if it were clear that there is a model structure on positive cochain complexes of R-modules for all R in which the fibrations are the epis. But from the statements that i am aware of at [[model structure on chain complexes]], in general the fibrations may be taken to be those epis that have injective kernels. For $R$ a field this is an empty condition and we are in business and find the familiar model structures. But for $R$ not a field? Notably simply $R = \mathbb{Z}$ What am I missing?

   added to injective object propositions and examples for injective modules and injective abelian groups

   P.S. I am checking if I am missing something: Toën on page 48/49 here behaves as if it were clear that there is a model structure on positive cochain complexes of R-modules for all R in which the fibrations are the epis. But from the statements that i am aware of at model structure on chain complexes, in general the fibrations may be taken to be those epis that have injective kernels. For $R$ a field this is an empty condition and we are in business and find the familiar model structures. But for $R$ not a field? Notably simply $R = \mathbb{Z}$ What am I missing?

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeAug 27th 2010
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   Author: TobyBartels
   Format: MarkdownItexI put the examples of categories with enough injectives *after* the examples of what injectives are in some of these categories.

   I put the examples of categories with enough injectives after the examples of what injectives are in some of these categories.