Replaced Lurie’s theorem on the existence of injective model structures with one derivable from Makkai-Rosicky that doesn’t need the enriching category to be “excellent”.

]]>Added Moser’s theorem about existence of both projective and injective model structures for all accessible model categories, which is much more general than Lurie’s (although it doesn’t imply that the injective model structure is cofibrantly generated, only that it is accessible).

]]>Uniformized the notation (D = small category, C = model category), separated the definition of the potential model structures from the theorems about their existence, and included some alternative existence theorems that don’t require cofibrant generation.

]]>Why does HTT Proposition A.3.3.2 (existence of injective and projective model structures on enriched diagram categories) require $\mathbf{S}$ to be excellent? In particular, why does it require the “invertibility hypothesis”? The proof isn’t written out but said to be “identical to that of Proposition A.2.8.2”, the existence of injective and projective model structures on unenriched diagram categories; I glanced at the latter proof but wasn’t able to see where the invertibility hypothesis might be used.

]]>I have added pointer to

Robert Piacenza,

*Homotopy theory of diagrams and CW-complexes over a category*, Can. J. Math. Vol 43 (4), 1991 (pdf)also chapter VI of Peter May et al.,

*Equivariant homotopy and cohomology theory*, 1996 (pdf)

to the entries *model structure on functors*, *Elmendorf’s theorem* and *Model categories of diagram spectra*.

I have edited the Properties-section at *model structure on functors* to make more explicit that all of the statements about functorial dependen on domain and codomain hold also for the case of $\mathbf{S}$-enriched functors on $\mathbf{S}$-enriched categories.

(This was previously mentioned in between the lines, but not made sufficiently explicit.)

]]>expanded model structure on functors by adding a long list of properties

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