On the unit of a monoidal model category (Q2352118)

The main result of this paper gives conditions under which a monoidal model structure may be replaced by another with the same weak equivalences but in which the unit is cofibrant. The author includes a number of examples in well-known cases of interest. The resulting model structures are generally different from standard known structures and the author remarks (p. 38) that they are generally ``not suitable to deal with commutative [monoid objects] precisely because the [unit] is cofibrant.'' The results are nevertheless interesting and presented in a straightforward manner.