Formalization of derived categories in Lean/mathlibArticleAuthors: Joël Riou
1
0009-0001-8932-7450
Joël Riou
This paper outlines the formalization of derived categories in the mathematical library of the proof assistant Lean 4. The derived category D(C) of any abelian category C is formalized as the localization of the category of unbounded cochain complexes with respect to the class of quasi-isomorphisms, and it is endowed with a triangulated structure.
Volume: Volume 1
Published on: July 15, 2025
Accepted on: February 11, 2025
Submitted on: May 17, 2024
Keywords: MSC 2020: 18G80, 18G15, 18G40, 18E35, 68V20, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT], [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [en] Derived category, Homological algebra, Spectral sequence