Why hom-functors are always cofibrant in the projective model structure in $[\cal T,\cal V]$? The claim is here on page 5.

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    $\begingroup$ This is probably using the assumption that all objects of $V$ are cofibrant. $\endgroup$ – Kevin Carlson Jan 23 '16 at 22:29
  • $\begingroup$ But natural transformations in $[\cal T,\cal V]$ are cofibrant if the components i.e. arrows in $\cal V$ are cofibrations,not objects.Moreover, projective model structure speak about fibrations,and not cofibrations. $\endgroup$ – user122424 Jan 24 '16 at 16:58
  • $\begingroup$ Cofibrant is an adjective that applies to objects, I have no idea what you mean by a cofibrant natural transformation. $\endgroup$ – Kevin Carlson Jan 24 '16 at 21:52

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