We discuss the properties of the supernova matter equation of state (EOS) including hyperons, and the emergence of hyperons in dynamical core-collapse processes. The recently tabulated EOS including hyperons is based on an SUf (3) extended relativistic mean field (RMF) model, in which the coupling constants of hyperons with scalar mesons are determined to fit the hyperon potential depths in nuclear matter, (UΣ, UΞ) = (+ 30 MeV, - 15 MeV), which are suggested from recent analyses of hyperon production reactions. Hyperon effects are found to be small in the core-collapse and bounce stages, but abundant hyperons appear when the temperature becomes high during black hole formation and promote earlier collapse of the accreting proto-neutron star. The maximum mass of a hot proto-neutron star is discussed, and we give a rough estimate of the critical mass of the accreting proto-neutron star, at which the proto-neutron star re-collapses to a black hole.
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