Comonoids, duality, and related displayed tech#584
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jajaperson wants to merge 18 commits intothe1lab:mainfrom
Draft
Comonoids, duality, and related displayed tech#584jajaperson wants to merge 18 commits intothe1lab:mainfrom
jajaperson wants to merge 18 commits intothe1lab:mainfrom
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Since duality of monoids and comonoids should be constructed as a functor
displayed over the isomorphism
$(\mathcal C^\mathrm{op})^\mathrm{op} \cong \mathcal C$, this refactors
`Cat.Base` slightly by removing the `C^op^op≡C` in favour of defining
the underlying isomorphism in a separate module, which can then be used
to define a path between precategories.
Also I sorted some imports.
So that we can use it without importing all the bicategory stuff.
For consistency with `Cat.Reasoning`.
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WIP
Description
This PR is working up to proving$\mathrm{Mon}(\mathcal C^\mathrm{op})^\mathrm{op}$ and $\mathrm{Comon}(\mathcal C)$ are equivalent as displayed categories. This has involved defining a lot of displayed machinery.
Checklist
Before submitting a merge request, please check the items below:
support/sort-imports.hs(ornix run --experimental-features nix-command -f . sort-imports).If your change affects many files without adding substantial content, and
you don't want your name to appear on those pages (for example, treewide
refactorings or reformattings), start the commit message and PR title with
chore:.Footnotes
Ahrens, Benedikt, and Peter LeFanu Lumsdaine. 2017. “Displayed Categories.” In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017), edited by Dale Miller, vol. 84. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSCD.2017.5. ↩