iblech/internal-methods
Notes on how to use the internal language of toposes in algebraic geometry
Why it is useful
internal-methods is a recent open-source project in Computer Algebra. It is included because it has recent repository activity and can support mathematical learning, research, modelling, software development, or AI workflows.
Repository at a glance
- Owner: iblech
- Primary language: TeX
- Latest update: 2026-07-17
- Stars / forks: 64 / 3
- License: Not specified
- Links: No separate project site was listed.
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Good starting points
- Read the project README and installation instructions.
- Try the smallest example before changing parameters or datasets.
- Check tests, issues, and release notes before relying on results in teaching or research.
- Cite the repository and its license when reusing code or figures.
README snapshot
Any scheme has its associated little and big Zariski toposes. These toposes support an internal mathematical language which closely resembles the usual formal language of mathematics, but is "local on the base scheme": For example, from the internal perspective, the structure sheaf looks like an ordinary local ring (instead of a sheaf of rings with local stalks) and vector bundles look like ordinary free modules (instead of sheaves of modules satisfying a local triviality condition). The translation of internal statements and proofs is facilitated by an easy mechanical procedure. We investigate how the internal language of the little Zariski