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Showing 1 to 3 of 3 for “"Synthetic Differential Geometry"”.
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Infinitesimal Models of Algebraic Theories
… the intuition when applied in the context of Synthetic Differential Geometry. This allows us to study well-known geometric structures and concepts from the viewpoint of infinitesimal geometric algebra. Infinitesimal models of algebraic theories generalise the notion of a model by allowing the …
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The functorial semantics of Lie theory
Ehresmann’s introduction of differentiable groupoids in the 1950s may be seen as a starting point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids and Lie groupoids) and sketch theory. This thesis uses tangent categories to build a bridge between these two …
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Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
We attempt to clarify and evaluate what shall be called Mac Lane’s thesis—the thesis that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard …