This is a pleasant but intentionally very elementary summary of the relevant concepts. If you're interested in much more on this, one place to start is MO (htt

This is a pleasant but intentionally very elementary summary of the relevant concepts. If you're interested in much more on this, one place to start is MO (https://mathoverflow.net/questions/4841/what-precisely-is-categorification https://mathoverflow.net/questions/4841/what-precisely-is-ca...), or the n-Category Café (https://golem.ph.utexas.edu/category/2008/10/what_is_categorification.html https://golem.ph.utexas.edu/category/2008/10/what_is_categor...), or Baez's TWF 121 (http://math.ucr.edu/home/baez/week121.html http://math.ucr.edu/home/baez/week121.html). Warning: all are much math-ier than Riehl's very nice slides, although the first one has enough content that you may find an answer that you like. If your math itch still isn't scratched, there's Baez and Dolan's paper "Categorification" (https://arxiv.org/abs/math/9802029 https://arxiv.org/abs/math/9802029). I don't know a programmer-focussed view on categorification; can anyone recommend one?