TITLE:
Synthetic Differential Geometry (SDG) of Stacks - Categorification of SDG
AUTHORS:
Hirokazu Nishimura
KEYWORDS:
Synthetic Differential Geometry, Categorification, Categorical Ambrose-Palais-Singer Theorem, Categorical Lie Algebra of Infinitesimal Endofunctors and Infinitesimal Natural Transformations, Categorical Differential Form
JOURNAL NAME:
Applied Mathematics,
Vol.17 No.8,
August
18,
2026
ABSTRACT: Orthodox synthetic differential geometry is concerned with microlinear spaces. This paper explains how to develop synthetic differential geometry of microlinear stacks or microlinear categories. As illustrations, we will address the categorical Lie algebra of infinitesimal endofunctors and infinitesimal natural transformations, the theory of differential forms and the categorified Ambrose-Palais-Singer theorem. In this paper, we use the word “stack” as a synonym of “category”.