Context. The post-main-sequence evolution of massive stars is very sensitive to many parameters of the stellar models. Key parameters are the mixing processes, the metallicity, the mass-loss rate, and the effect of a close companion. Aims. We study the change in the red supergiant (RSG) lifetimes, the tracks in the Hertzsprung-Russel diagram (HRD), the positions in this diagram of the pre-supernova progenitor and the structure of the stars at that time for various mass-loss rates during the RSG phase and for two different initial rotation velocities. Methods. Stellar models were computed with the Geneva code for initial masses between 9 and 25 M at solar metallicity (Z = 0.014) with 10 times and 25 times the standard mass-loss rates during the RSG phase, with and without rotation. Results. The surface abundances of RSGs are much more sensitive to rotation than to the mass-loss rates during that phase. A change of the RSG mass-loss rate has a strong impact on the RSG lifetimes and in turn on the luminosity function of RSGs. An observed RSG is associated with a model of higher initial mass when models with an enhanced RSG mass-loss rate are used to deduce that mass. At solar metallicity, models with an enhanced mass-loss rate produce significant changes in the populations of blue, yellow, and RSGs. When extended blue loops or blueward excursions are produced by enhanced mass-loss, the models predict that a majority of blue (yellow) supergiants are post-RSG objects. These post-RSG stars are predicted to show much lower surface rotational velocities than similar blue supergiants on their first crossing of the HR gap. Enhanced mass-loss rates during the RSG phase have little impact on the Wolf-Rayet populations. The position in the HRD of the end point of the evolution depends on the mass of the hydrogen envelope. More precisely, whenever at the pre-supernova stage the H-rich envelope contains more than about 5% of the initial mass, the star is a RSG, and whenever the H-rich envelope contains less than 1% of the total mass, the star is a blue supergiant. For intermediate situations, intermediate colors and effective temperatures are obtained. Yellow progenitors for core-collapse supernovae can be explained by models with an enhanced mass-loss rate, while the red progenitors are better fitted by models with the standard mass-loss rate.

The rotation of stars has many interesting and important consequences for the photometric and chemical evolution of galaxies. Many of the predictions of models of stellar rotation are now compared with observations of surface abundances and velocities, with interferometric studies of fast rotating stars, with internal rotation profiles as they can be deduced by asteroseismology, to cite just a few observational constraints. In this paper, we investigate how the outputs of models depend on the prescriptions used for the diffusion coefficients included in the shellular rotating models. After recalling the various prescriptions found in the literature, we discuss their impacts on the evolutionary tracks and lifetimes of the Main-Sequence (MS) phase, the changes of the surface composition and velocities during the MS phase, the distribution of the core helium lifetime in the blue and the red part of the HR diagram, the extensions of the blue loops, the evolution of the angular momentum of the core, and the synthesis of primary nitrogen in fast-rotating metal-poor