Syzygies and higher groupoids

It has always been somewhat strange to me how popular category theory and infinity-category theory are on the 'mathematical internet', despite how few working mathematicians actually need them. However, over the past decade, infinity categories have grown in importance in more classical mathematics research -- especially in my own field of arithmetic geometry! My friend and I wrote a blog post on infinity groupoids -- these are to infinity categories as sets are to ordinary categories. The goal of the blog post was to show, in as elementary a way as possible, what uses infinity groupoids have, to try and give readers a taste of why they've become so helpful in modern mathematics. hidden-phenomena.com/articles/anima As a sneak peak: groupoids are, in some situations, a more convenient object than sets for handling group actions!