Axiomatic differential geometry. III-2 -- its landscape. II: Model theory. II

zbMATH Open1281.51013arXiv1209.6109MaRDI QIDQ2844352

Hirokazu Nishimura

Publication date: 28 August 2013

Published in: Far East Journal of Mathematical Sciences (Search for Journal in Brave)

Abstract: Given a complete and (locally) cartesian closed category U, it is shown that the category of functors from the category of Weil algebras to the category U is (locally, resp.) cartesian closed. The corresponding axiomatization for differential geometry based upon Weil functors is then given.

Full work available at URL: https://arxiv.org/abs/1209.6109

zbMATH Keywords

synthetic differential geometryCartesian closedDG-categoryaxiomatic differential geometrylocally Cartesian closed

Mathematics Subject Classification ID

Distance geometry (51K99) Categories in geometry and topology (18F99) Synthetic differential geometry (51K10) Topos-theoretic approach to differentiable manifolds (58A03)

Related Items (2)

Axiomatic differential geometry II-2 - differential forms ⋮ Axiomatic differential geometry. III-1 -- its landscape. I: Model theory. I

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