Can fertilizer be classified as vegan? If so, what requirements are imposed on it? Is it enough to say that no animal products can be used, or is the discussion more nuanced for fertilizer?
For a fertilizer to be called vegan, it has to contain no animal products. While debatable, I would guess that animal poo would be considered as an animal product as well, so it would have to not contain that.
Your best shot at having a vegan fertilizer is to make one yourself by composting the leftovers from your vegetables and fruits. If you have a garden (which I suppose you do, if you want a fertilizer) there is a chance of a small number of bugs living and dying in your compost but whether that is a price you are willing to pay is up to you.
Another vegan fertilizer alternative would be wholly synthetic, mineral fertilizer - just make sure it does not use anything vaguely sounding or obviously non-vegan. If in doubt, contact producer or choose one advertised as vegan.
Yes -- there is plenty of vegan fertilizers.
Compost (aka Black Gold) made from food scraps (eg corn cobs, onion ends, pea pods, leafy stems, potato peels, etc) and tree leaves is an excellent vegan fertilizer.
Humanure, if consensual, is also vegan. It's a great alternative to using animal manure as fertilizer and also more ecological than pit latrines, cesspools, or sewage "treatment" plants that routinely dump raw sewage into rivers and oceans.
There's over 8 billion humans on earth, so we have no shortage of humanure fertilizer.