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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 27th 2010

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?

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeAug 27th 2010

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