https://peertube.wtf/videos/watch/df45cb12-941e-4293-b718-069d8d78d67c Abstract: I will discuss one part of my PhD thesis, in which I provide a categorification of the notion of a mathematical structure originally given by Bourbaki in their set theory textbook. The main result is that any isomorphism-invariant property of a finite structure can be checked by computing the number of isomorphic copies of small substructures it contains. A special case of this theorem is the classical result of Hilbert about elementary symmetric polynomials generating the algebra of all symmetric polynomials. I will also discuss how the logical complexity of a positive formula controls the size of the small substructures one must count. Slides: https://aten.cool/documents/slides/Aten_New_York_Category_Seminar_2024.pdf Tue, 18 Aug 2026 12:29:38 GMT https://validator.w3.org/feed/docs/rss2.html PeerTube - https://peertube.wtf https://peertube.wtf/lazy-static/avatars/45856119-df14-4b5f-bff8-4807ae2cfbd2.png https://peertube.wtf/videos/watch/df45cb12-941e-4293-b718-069d8d78d67c All rights reserved, unless otherwise specified in the terms specified at https://peertube.wtf/about and potential licenses granted by each content's rightholder.