I looked down and didn't see anything, but as I looked back up, there was a small, yearling cat of some generic dark color running ahead of me. It ran ahead of me up to the corner and we turned the corner together. I was still surprised and didn't really piece it together yet (and in fact sailed around the corner without looking -- good thing nobody else was coming). Once we rounded the corner, the cat ran ahead of me, going a good deal faster than I was biking.
At about this point I realized I had run over the cat, and it was what I had felt through the bottoms of my shoes. It must have come out of some side alley (there are a million tiny alleys and gaps in Japan that cats can disappear into), sensed me coming, and lit out running -- unfortunately right into me. However, whatever part of the cat I had run over, it didn't affect the cat much, witness it's fast flight from me now.
"Oh neko-chan" I said with instinctive concern... but Mr. Neko had by now disappeared into another of Tokyo's nooks, and I looked for it in vain as I passed by.
There must be something about animals here, maybe it's nothing more than the narrow streets. I ran over a pigeon last year in Japan, something else I'd never done in my life before coming here.