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Grids of stellar models with rotation II. WR populations and supernovae/GRB progenitors at Z = 0.014

We used a recent grid of stellar models computed with and without rotation to make predictions concerning the WR populations and the frequency of different types of core-collapse SNe. Current rotating models were checked to provide good fits to the following features: solar luminosity and radius at the solar age, main-sequence width, red-giant and red-supergiant (RSG) positions in the HRD, surface abundances, and rotational velocities. Rotating stellar models predict that about half of the observed WR stars and at least half of the type Ibc SNe may be produced through the single-star evolution channel. Rotation increases the duration of the WNL and WNC phases, while reducing those of the WNE and WC phases, as was already shown in previous works. Rotation increases the frequency of type Ic SNe. The upper mass limit for type II-P SNe is \sim 19.0 MSun for the non rotating models and \sim 16.8 MSun for the rotating ones. Both values agree with observations. Moreover, present rotating models provide a very good fit to the progenitor of SN 2008ax. We discuss future directions of research for further improving the agreement between the models and the observations. We conclude that the mass-loss rates in the WNL and RSG phases are probably underestimated at present. We show that up to an initial mass of 40 M\odot, a surface magnetic field inferior to about 200 G may be sufficient to produce some braking. Much lower values are needed at the red supergiant stage. We suggest that the presence/absence of any magnetic braking effect may play a key role in questions regarding rotation rates of young pulsars and the evolution leading to LGRBs.