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One of the main new features of synthetic differential geometry, as opposed to classical geometry, is the existence of infinitesimal spaces such as D, D 2, D × D, etc. These spaces essentially allow us to give alternative, algebraic approaches to geometric notions which are classically defined by limit processes. For example, exterior differentiation of a form is interpreted geometrically via circulation along an n-cube, a notion which involves integrals. In Chapter IV, on the other hand, we saw how to define exterior differentiation via circulation along an infinitesimal n-cube, and no actual integration was needed in this definition.

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© 1991 Springer Science+Business Media New York

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Moerdijk, I., Reyes, G.E. (1991). Connections on Microlinear Spaces. In: Models for Smooth Infinitesimal Analysis. Springer, New York, NY.

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3095-8

  • Online ISBN: 978-1-4757-4143-8

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