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Finite-temperature equation of state (EoS) and the composition of densenuclear and hypernuclear matter under conditions characteristic of neutron starbinary merger remnants and supernovas are discussed. We consider both neutrinofree-streaming and trapped regimes which are separated by a temperature of afew MeV. The formalism is based on covariant density functional (CDF) theoryfor the full baryon octet with density-dependent couplings, suitably adjustedin the hypernuclear sector. The softening of the EoS with the introduction ofthe hyperons is quantified under various conditions of lepton fractions andtemperatures. We find that $\Lambda$, $\Xi^-$, and $\Xi^0$ hyperons appear inthe given order with a sharp density increase at zero temperature at thethreshold being replaced by an extended increment over a wide density range athigh temperatures. The $\Lambda$ hyperon survives in the deep subnuclearregime. The triplet of $\Sigma$s is suppressed in cold hypernuclear matter upto around seven times the nuclear saturation density, but appears insignificant fractions at higher temperatures, $T\geq 20$ MeV, in both supernovaand merger remnant matter. We point out that a special isospin degeneracy pointexists where the baryon abundances within each of the three isospin multipletsare equal to each other as a result of (approximate) isospin symmetry. At thatpoint, the charge chemical potential of the system vanishes. We find that underthe merger remnant conditions, the fractions of electron and $\mu$-on neutrinosare close and are about 1\%, whereas in the supernova case, we only find asignificant fraction ($\sim$10\%) of electron neutrinos, given that in thiscase, the $\mu$-on lepton number is zero.

Equation of state and composition of proto-neutron stars and merger remnants with hyperons