I remember my early days on two wheels, before I started doing such work. Trying to ride up a bicycle access ramp to the top of the levee had me wavering all over the ramp. I could hardly keep the bike under control. I also noticed that I couldn't ride very long before I'd go sway-backed. Sagging abs, I've no doubt.
At some point in 2014 I finally began to do regular off-bike work. I didn't want to pay for a gym membership, and going to the gym would only be something else to cram into my day. Gyms tend to be noisy places, too. I decided to do my off-bike work at home.
My off-bike program consists of flexibility exercises; arm/upper body exercises; core work ; and lower body/leg work. Some, such as "chair bend" (flexibility) and "bird dog" (which I class as a lower body exercise) are taken from Selene Yeager's book, Every Woman's Guide to Cycling. So is "push-up row" (arms).
Others are some exercises I was given to do way back in about 2010, when a loose toe cage on my trike's left pedal resulted in strained tendons. One of these is "straight leg raise" (legs). After some months I began to do this exercise with a small weight resting on my leg just above the knee. Good work for the abs, I guess, which would seem to put this exercise under core work.
I also have two core workouts. Core I is taken from Kelly Cycling. Core II is from another of Selene Yeager's books, Get Fast!
Over time I've progressed from using two-pound weights to lifting five-pound weights. Maybe some day I'll get a pair of small adjustable-weight dumbbells. There are days when I feel as though I'm about ready to heft increased weight for these exercises. Not too much, though! I must remember that this is resistance training -- not body building.