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The early and complete temporal characterization of optical, fast, transient sources requires continuous and multiband observations over different timescales (hours to months). For time-domain astronomy, using several telescopes to analyze single objects is the usual method, allowing the acquisition of highly sampled light curves. Taking a series of images each night helps to construct an uninterrupted chain of observations with a high cadence and low duty cycle. Speed is paramount, especially at early times, in order to capture early features in the light curve that help determine the nature of the observed transients and assess their astrophysical properties. However, the problem of rapidly extracting source properties (temporal and color evolution) with a heterogeneous data set remains. Consequently, we present Muphoten, a general and fast-computation photometric pipeline able to address these constraints. It is suitable for extracting transient brightness over multi-telescope and multiband networks to create a single homogeneous photometric time series. We show the performance of Muphoten with observations of the optical transient SN 2018cow (from 2018 June to 2018 July), monitored by the GRANDMA network and with the publicly available data of the Liverpool Telescope.