THE LARGE STRUCTURES OF GROTHENDIECK FOUNDED ON FINITE ORDER ARITHMETIC https://arxiv.org/pdf/1102.1773.pdf
cohomology toposes ZFC Zermelo Fraenkel set theory with Choice
theorems of EGA and SGA finite order arithmetic elementary topos of sets with infinity arithmetic scheme category of sheaves
Finite order arithmetic, or simple type theory with infinity, is n-th order arithmetic for all finite n.
universe
theory of classes and collections conservative over set theory
derived categories
fibered categories
replacement ZFC
ETCS Elementary Theory of the Category of Sets
Equiconsistency of finite order arithmetic