Forms and exterior differentiation in Cartesian differential categories

G.S.H. Cruttwell

Cartesian differential categories abstractly capture the notion of a differentiation operation. In this paper, we develop some of the theory of such categories by defining differential forms and exterior differentiation in this setting. We show that this exterior derivative, as expected, produces a cochain complex.

Keywords: Cartesian differential categories, Differential forms, Exterior derivative, de Rham cohomology

2010 MSC: 18D99, 53A99

Theory and Applications of Categories, Vol. 28, 2013, No. 28, pp 981-1001.

Published 2013-10-09.

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