# Questions tagged [synthetic-differential]

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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### Constructions with Superschemes via Kan extensions

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### Geometric intuition for $R[x,y]/ (x^2,y^2)$, kinematic second tangent bundle, and Wraith axiom

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### Examples of connection preserving maps in differential geometry

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### Making area/volume calculations that use SIA rigorous

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### Intuition and analogue of Wraith axiom from synthetic differential geometry

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### Constructing computable synthetic differential geometry?

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### The (co)tangent sheaf of a topological space

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### Differential algebraic geometry vs Diffiety theory

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### Constructive analysis and synthetic differential geometry

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### Query about SDG (Synthetic Differential Geometry)

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### Relationship between synthetic differential geometry and differential cohesion?

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### Semi-holonomic jets in synthetic differential geometry

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### Is integration smooth?

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### Characterization of formally étale morphisms between microlinear objects?

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### What is meant by the inverse function theorem in algebraic geometry?

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### Internal characterizations of lifting properties?

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### When are descriptions of formal unramifiedness/smoothness via lifting properties equivalent to those via induced arrows to pullbacks?

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### Local diffeomorphism (étale maps) in terms of infinitesimal tubular neighborhood?

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### Competing notions of formal étaleness

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### Étale morphisms in SDG

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### Intuition for the Cartan connection and "rolling without slipping" in Cartan geometry

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### Resources on a smooth topos containing complex analytic/holomorphic geometry

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### Lie functor preserves "surjections" in synthetic differential geometry?

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### Jets in synthetic differential geometry

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