Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 369381 (2008) 

Curvature in synthetic differential geometry of groupoidsHirokazu NishimuraInstitute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 3058571, Japan, email:logic {\em at} math.tsukuba.ac.jpAbstract: We study the fundamental properties of curvature in groupoids within the framework of synthetic differential geometry. As is usual in synthetic differential geometry, its combinatorial nature is emphasized. In particular, the classical Bianchi identity is deduced from a combinatorial version of it. Keywords: Curvature, synthetic differential geometry, second Bianchi identity, combinatorial Bianchi identity, groupoids Classification (MSC2000): 51K10 Full text of the article:
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