https://github.com/b-mehta/topos
Topos theory in lean
https://github.com/b-mehta/topos
leanprover topos-theory
Last synced: 6 months ago
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Topos theory in lean
- Host: GitHub
- URL: https://github.com/b-mehta/topos
- Owner: b-mehta
- Created: 2020-02-16T18:27:48.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2021-01-06T04:29:03.000Z (over 4 years ago)
- Last Synced: 2024-11-28T23:31:28.451Z (6 months ago)
- Topics: leanprover, topos-theory
- Language: Lean
- Size: 3.39 MB
- Stars: 56
- Watchers: 9
- Forks: 2
- Open Issues: 8
-
Metadata Files:
- Readme: README.md
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README
# Topos theory for Lean
This repository contains formal verification of results in Topos Theory, drawing from "Sheaves in Geometry and Logic" and "Sketches of an Elephant".
## What's here?
- Cartesian closed categories
- Sieves and grothendieck topologies including the open set topology
- (Trunc) construction of finite products from binary products and terminal
- Locally cartesian closed categories and epi-mono factorisations
- Many lemmas about pullbacks (for instance the pasting lemma)
- Skeleton of a category (assuming choice)
- Subobject category
- Subobject classifiers and power objects
- Reflexive monadicity theorem
- (Internal) Beck-Chevalley and Pare's theorem
- Definition of a topos
- Every topos is finitely cocomplete
- Local cartesian closure of toposes and Fundamental Theorem of Topos Theory
- Lawvere-Tierney topologies and sheaves
- Sheafification of LT topologies
- Proof that Lawvere-Tierney topologies generalise Grothendieck topologies
## What's coming soon?
- Proof that category of coalgebras for a comonad form a topos
- Logical functors
- Logic internal to a topos
- Natural number objects
## What might be coming?
- Geometric morphisms
- Filter/quotient construction on a topos
- ETCS
- The construction of the Cohen topos to show ZF doesn't prove CH
- The construction of a topos to show ZF doesn't prove AC
- A topos in which every function R -> R is continuous
- Giraud's theorem
- Classifying toposes
## Build Instructions
EITHER:
[Install lean and leanproject](https://leanprover-community.github.io/get_started.html#regular-install).
OR:
If you have docker, spin up an instance of the `edayers/lean` image (or build your own using the provided Dockerfile).
FINALLY:
run
``` sh
leanproject get b-mehta/topos
leanproject build
```