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Given an equivalence `F : C ⥤ D` of categories, and a monoidal structure on `C`, there is a (essentially unique?) monoidal structure on `D` making `F` a monoidal functor.
(Thanks @rwbarton for [sug…
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On Slack, @kris-brown asks how to do preorders in Catlab. In fact, it would be good to add signatures and syntax systems for preorders and also thin categories to the standard library.
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@rmatthes has introduced a dependency of package CategoryTheory on (some files of) the package Bicategories.
While I agree that it is conceptually undesirable to separate the two, this dependency m…
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The following final derivations are inconsistent: https://github.com/homalg-project/CAP_project/blob/8c610224cd4a24adb2e9f69b6bcd25e0eb00d5e5/MonoidalCategories/gap/RigidSymmetricClosedMonoidalCategor…
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I suggest the following changes to the CategoryTheory library:
1. The homs-are-sets assumption should be re-integrated into the definition of precategories.
2. The definition of isomorphism should be …
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Related to #35 .
So in branch Strict, I implemented a lot of Strict category theory, with a particular design in mind: That `Category` itself wouldn't be parametrized by an equality, but would use …
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We should provide some examples of monoidal categories. The absolutely fundamental ones are:
* [x] `Type` (done in [a branch](https://github.com/leanprover-community/mathlib/blob/monoidal-types/src/c…
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While reviewing the implementation of `torch.linalg.trace` https://github.com/pytorch/pytorch/pull/62714#discussion_r778833069, we realised that `linalg.trace` supports non-square matrices.
This sh…
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We should add Bipartitioned graphs to `Catlab.Graphs`. We can then use this type for both AlgebraicPetri.jl and also be able to represent presentations that would give us pushout support for combining…
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ACT has a nice story to tell about linear algebra, through at least two paths:
- [Graphical linear algebra](https://graphicallinearalgebra.net/) and the [category of linear relations](https://arxiv…