Charlotte Aten --- Invariants of structures.
Автор: The New York City Category Theory Seminar
Загружено: 2024-12-04
Просмотров: 217
A Zoom talk given on December 4th, 2024.
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.
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