I've been looking at some definitions of Grothendieck rings. However I've not found a good definition that I've understood. Any recommendations? I'm referring to the definition in tensor categories, more specifically I've discovered there are some structure coefficients in a Grothendieck Ring, I understand the mathematics from a physics perspective. I learned this first from Physics papers, but I want to understand more deeply the mathematical structure. http://www.math.sunysb.edu/~kirillov/tensor/tensor.html is the set of lecture notes I'm referring to, and I'd love if someone could help me tag this post more effectively.