http://en.wikipedia.org/wiki/Supernova_remnant"The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and shocks along the way."
And to quote from the Supernova article you posted:
"The remnant of a supernova explosion consists of a compact object and a rapidly expanding shock wave of material."
A supernova remnant is mainly a shockwave, and will not leave a nebula were the center has any significant mass except the very core (black hole, neutron star or similar).
Within the system of Capella, there won't be matter with a significant density (probably not or only a little higher than it was before the supernova) within weeks. The matter ejected by the supernova will reach interstellar medium unhindered within 10-1000 years:
"An SNR passes through the following stages as it expands:
1. Free expansion of the ejecta, until they sweep up their own weight in circumstellar or interstellar medium. This can last tens to a few hundred years depending on the density of the surrounding gas."
Ok, some supernova remnants are named nebula (the "crab nebula") while others are not (
Cassiopeia A)
True, didn't know that.