Category Theory in SageMath

[Frank Zenter]

For teaching purposes, I look for a tool which allows the manipulation of functor-categories (toposes) indexed by finitely presented categories in order to illustrate the concepts “category”,“functor” and “natural transformation”. In particular, it should allow the construction of limits, colimits, Kan-extensions, function objects, subobject-classifyer etc. in such categories and all their relations (c.f. W. Lavwere:  [Conceptual mathematics](https://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categories/dp/052171916X)).

Is there such a Sage-tool (similar to the ones for [differential geometry](http://doc.sagemath.org/html/en/reference/manifolds/index.html) or [algebraic topology](http://doc.sagemath.org/html/en/reference/homology/index.html)) or is one planned?

[Dima Pasechnik]

http://homalg-project.github.io/CAP_project/

is the only thing that comes to mind.

GAP is a part of Sagemath, and so you can install the corr. packages there

(or in a stand-alone GAP)

On Mon, 3 Sep 2018, 20:57 Frank Zenter, <zen...@gmail.com> wrote:

For teaching purposes, I look for a tool which allows the manipulation of functor-categories (toposes) indexed by finitely presented categories in order to illustrate the concepts “category”,“functor” and “natural transformation”. In particular, it should allow the construction of limits, colimits, Kan-extensions, function objects, subobject-classifyer etc. in such categories and all their relations (c.f. W. Lavwere:  [Conceptual mathematics](https://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categories/dp/052171916X)).

Is there such a Sage-tool (similar to the ones for [differential geometry](http://doc.sagemath.org/html/en/reference/manifolds/index.html) or [algebraic topology](http://doc.sagemath.org/html/en/reference/homology/index.html)) or is one planned?

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