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How galaxies form, assemble, and cease their star-formation is a centralquestion within the modern landscape of galaxy evolution studies. Theseprocesses are indelibly imprinted on the galaxy stellar mass function (SMF). Wepresent constraints on the shape and evolution of the SMF, the quiescent galaxyfraction, and the cosmic stellar mass density across 90% of the history of theUniverse from $z=7.5\rightarrow0.2$ via the COSMOS survey. Now with deeper andmore homogeneous near-infrared coverage exploited by the COSMOS2020 catalog, weleverage the large 1.27 deg$^{2}$ effective area to improve sample statisticsand understand cosmic variance particularly for rare, massive galaxies and pushto higher redshifts with greater confidence and mass completeness than previousstudies. We divide the total stellar mass function into star-forming andquiescent sub-samples through $NUVrJ$ color-color selection. Measurements arethen fitted with Schechter functions to infer the intrinsic SMF, the evolutionof its key parameters, and the cosmic stellar mass density out to $z=7.5$. Wefind a smooth, monotonic evolution in the galaxy SMF since $z=7.5$, inagreement with previous studies. The number density of star-forming systemsseems to have undergone remarkably consistent growth spanning four decades instellar mass from $z=7.5\rightarrow2$ whereupon high-mass systems becomepredominantly quiescent (i.e. downsizing). An excess of massive systems at$z\sim2.5-5.5$ with strikingly red colors, some newly identified, increase theobserved number densities to the point where the SMF cannot be reconciled witha Schechter function. Systematics including cosmic variance and/or AGNcontamination are unlikely to fully explain this excess, and so we speculatethat there may be contributions from dust-obscured objects similar to thosefound in FIR surveys. (abridged)

COSMOS2020: The Galaxy Stellar Mass Function: the assembly and star formation cessation of galaxies at $0.2\lt z \leq 7.5$