Originally Posted by
eugenek
I would put emphasis on "in multiple fitness realms." Running and cycling are not multiple fitness realms. Cycling and strength training for your legs are, but there are many studies showing that trying to cross-train the same muscle group for strength and endurance at the same time is very tricky and potentially futile (there is a substantial risk of "interference" where different types of training inhibit each other).
The best and safest kind of cross training is endurance cycling and core & upper body strength training.
and there are no indications that having a stronger core makes you a faster cyclist. in fact in recent studies regarding weight lifting and cyclists (with the exception of track sprint specialists) indications are that at best it doesn't hurt (ones cycling) and at worst it actually makes one slower.