cat/CHANGELOG.md

Change log

Version 1.6.0

This version mainly contains changes to the report.

This is the version I submit for my MSc..

Version 1.5.0

Prove postulates in Cat.Wishlist:

• ntypeCommulative : n ≤ m → HasLevel ⟨ n ⟩₋₂ A → HasLevel ⟨ m ⟩₋₂ A

Prove that these two formulations of univalence are equivalent:

∀ A B → isEquiv (A ≡ B) (A ≅ B) (id-to-iso A B)
∀ A   → isContr (Σ[ X ∈ Object ] A ≅ X)

Prove univalence for the category of...

• the opposite category
• sets
• "pair" category

Finish the proof that products are propositional:

• isProp (Product ...)
• isProp (HasProducts ...)

Remove --allow-unsolved-metas pragma from various files

Also renamed a lot of different projections. E.g. arrow-composition, etc..

Version 1.4.1

Defines a module to work with equivalence providing a way to go between equivalences and quasi-inverses (in the parlance of HoTT).

Finishes the proof that the category of homotopy-sets are univalent.

Defines a custom "prelude" module that wraps the cubical library and provides a few utilities.

Reorders Category.isIdentity such that the left projection is left identity.

Include some text for the half-time report.

Renames IsProduct.isProduct to IsProduct.ump to avoid ambiguity in some circumstances.

[WIP]: Adds some stuff about propositionality for products.

Version 1.4.0

Adds documentation to a number of modules.

Adds an "equality principle" for categories and monads.

Prove that IsMonad is a mere proposition.

Provides the yoneda embedding without relying on the existence of a category of categories. This is achieved by providing some of the data needed to make a ccc out of the category of categories without actually having such a category.

Renames functors object map and arrow map to omap and fmap.

Prove that Kleisli- and monoidal- monads are equivalent!

[WIP] Started working on the proofs for univalence for the category of sets and the category of functors.

Version 1.3.0

Removed unused modules and streamlined things more: All specific categories are in the name space Cat.Categories.

Lemmas about categories are now in the appropriate record e.g. IsCategory. Also changed how category reexports stuff.

Rename the module Properties to Yoneda - because that's all it talks about now.

Rename Opposite to opposite

Add documentation in Category-module

Formulation of monads in two ways; the "monoidal-" and "Kleisli-" form.

WIP: Equivalence of these two formulations

Also use hSets in a few concrete categories rather than just pure Set.

Version 1.2.0

This version is mainly a huge refactor.

I've renamed

• distrib to isDistributive
• arrowIsSet to arrowsAreSets
• ident to isIdentity
• assoc to isAssociative

And added "type-synonyms" for all of these. Their names should now match their type. So e.g. isDistributive has type IsDistributive.

I've also changed how names are exported in Functor to be in line with Category.

Version 1.1.0

In this version categories have been refactored - there's now a notion of a raw category, and a proper category which has the data (raw category) as well as the laws.

Furthermore the type of arrows must be homotopy sets and they must satisfy univalence.

I've made a module Cat.Wishlist where I just postulate things that I hope to implement upstream in cubical.

I have proven that IsCategory is a mere proposition.

I've also updated the category of sets to adhere to this new definition.