cat/CHANGELOG.md

Change log
=========

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.