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edited Oct 29, 2013 at 11:22

Some not very clever questions on closed model categories.

For a (left or right) Quillen functor $F:C\to D$ what arguments does one usually use for proving that $Ho F$ is fully faithful when restricted to a full subcategory $C'$ of $C$$Ho C$? I suspect that there should exist some very 'classical' reasonings of this sort.
I would like to study the duals of motivic homotopy categories, so my categories are fibrantly cogenerated. Where could I find some information on the properties of such categories (in particular, on the existence of Bousfield localizations)? A related question: which notions of the model category theory are self-dual (even if they do not 'look to be so')?
How could one prove that a fibrantly cogenerated model category is a spectral one in the sense of the paper: Schwede, Stefan(D-MUNS-GFM); Shipley, Brooke(1-PURD) Stable model categories are categories of modules. (English summary) Topology 42 (2003), no. 1, 103–153?

Some not very clever questions on closed model categories.

For a (left or right) Quillen functor $F:C\to D$ what arguments does one usually use for proving that $Ho F$ is fully faithful when restricted to a full subcategory $C'$ of $C$? I suspect that there should exist some very 'classical' reasonings of this sort.
I would like to study the duals of motivic homotopy categories, so my categories are fibrantly cogenerated. Where could I find some information on the properties of such categories (in particular, on the existence of Bousfield localizations)? A related question: which notions of the model category theory are self-dual (even if they do not 'look to be so')?
How could one prove that a fibrantly cogenerated model category is a spectral one in the sense of the paper: Schwede, Stefan(D-MUNS-GFM); Shipley, Brooke(1-PURD) Stable model categories are categories of modules. (English summary) Topology 42 (2003), no. 1, 103–153?

Some not very clever questions on closed model categories.

For a (left or right) Quillen functor $F:C\to D$ what arguments does one usually use for proving that $Ho F$ is fully faithful when restricted to a full subcategory $C'$ of $Ho C$? I suspect that there should exist some very 'classical' reasonings of this sort.
I would like to study the duals of motivic homotopy categories, so my categories are fibrantly cogenerated. Where could I find some information on the properties of such categories (in particular, on the existence of Bousfield localizations)? A related question: which notions of the model category theory are self-dual (even if they do not 'look to be so')?
How could one prove that a fibrantly cogenerated model category is a spectral one in the sense of the paper: Schwede, Stefan(D-MUNS-GFM); Shipley, Brooke(1-PURD) Stable model categories are categories of modules. (English summary) Topology 42 (2003), no. 1, 103–153?

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asked Oct 29, 2013 at 4:53

On closed model categories: standard arguments and fibrantly cogenerated categories

Some not very clever questions on closed model categories.

For a (left or right) Quillen functor $F:C\to D$ what arguments does one usually use for proving that $Ho F$ is fully faithful when restricted to a full subcategory $C'$ of $C$? I suspect that there should exist some very 'classical' reasonings of this sort.
I would like to study the duals of motivic homotopy categories, so my categories are fibrantly cogenerated. Where could I find some information on the properties of such categories (in particular, on the existence of Bousfield localizations)? A related question: which notions of the model category theory are self-dual (even if they do not 'look to be so')?
How could one prove that a fibrantly cogenerated model category is a spectral one in the sense of the paper: Schwede, Stefan(D-MUNS-GFM); Shipley, Brooke(1-PURD) Stable model categories are categories of modules. (English summary) Topology 42 (2003), no. 1, 103–153?