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The Transiting Exoplanet Survey Satellite (TESS) mission has provided photometric light curves for stars across nearly the entire sky. This allows for the application of asteroseismology to a pool of potential solar-like oscillators that is unprecedented in size. We aim to produce a catalogue of solar-like oscillators observed by TESS in the 120-second and 20-second cadence modes. The catalogue is intended to highlight stars oscillating at frequencies above the TESS 30-minute cadence Nyquist frequency with the purpose of encompassing the main sequence and subgiant evolutionary phases. We aim to provide estimates for the global asteroseismic parameters $ν_{\mathrm{max}}$ and $Δν$. We apply a new probabilistic detection algorithm to the 120-second and 20-second light curves of over 250,000 stars. This algorithm flags targets that show characteristic signatures of solar-like oscillations. We manually vet the resulting list of targets to confirm the presence of solar-like oscillations. Using the probability densities computed by the algorithm, we measure the global asteroseismic parameters $ν_{\mathrm{max}}$ and $Δν$. We produce a catalogue of 4,177 solar-like oscillators, reporting $Δν$ and $ν_{\mathrm{max}}$ for $98\%$ of the total star count. The asteroseismic data reveals vast coverage of the HR diagram, populating the red giant branch, the subgiant regime and extending toward the main sequence. A crossmatch with external catalogs shows that 25 of the detected solar-like oscillators are a component of a spectroscopic binary, and 28 are confirmed planet host stars. These results provide the potential for precise, independent asteroseismic constraints on these and any additional TESS targets of interest.