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Synthetic differential geometry is an axiomatic formulation of differential geometry in smooth toposes. The axioms ensure that a well-defined notion of infinitesimal spaces exists in the topos, whose existence concretely and usefully formalizes the wide-spread but often vague intuition about the role of infinitesimals in differential geometry.
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Resources on a smooth topos containing complex analytic/holomorphic geometry
In this question Urs Schreiber mentioned there are models in synthetic differential geometry of complex analytic geometry.
First of all: When Urs writes complex analytic geometry, does he mean comple …