Blazars are extremely variable objects emitting radiation across the electromagnetic spectrum and showing variability on time scales from minutes to years. Simultaneous multi-wavelength observations are crucial for understanding the emission mechanisms. In particular the study of their TeV emission is relevant to test the dominant radiative process at such energies (e.g. leptonic models predict a correlation between X-ray and TeV emission). As well, the correlation with the bump at low energy or the possible common detection with a neutrino signal can be relevant to constrain the physical model. From radio via optical and from X-ray to gamma rays, a variety of instruments, as OVRO and Fermi, are already monitoring blazars. At TeV energies, long-term monitoring is currently carried out by HAWC and FACT. Towards 24/7 continuous observations, the goal is to have similar monitoring telescopes at locations around the globe in order to close temporal gaps and compile light curves with homogeneous sensitivity. With the M@TE (Monitoring at TeV energies) project, we are planning to install an Imaging Air Cherenkov Telescope equipped with an improved version of the FACT camera and the mechanical structure of one of the mounts of the HEGRA experiment at the site of San Pedro Mártir in Mexico. Featuring excellent observation conditions, this location provides a variety of instruments from radio to optical wavelength allowing for coordinated multi-wavelength blazar studies. In this work, we will present the status of the project.