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Univalent groupoids - #651

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univalent-groupoids
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TOTBWF wants to merge 7 commits into
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univalent-groupoids

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@TOTBWF

@TOTBWF TOTBWF commented Jul 20, 2026

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Description

This PR defines univalent groupoids, proves that they are equivalent to univalent pregroupoids, and also establishes that
some existing categories are univalent pregroupoids.

It also contains a minor optimization to right-inverse→equiv and left-inverse→equiv that avoids incurring a transport
on the inverse map.

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Before submitting a merge request, please check the items below:

  • I've read the contributing guidelines.
  • The imports of new modules have been sorted with support/sort-imports.hs (or nix run --experimental-features nix-command -f . sort-imports).
  • All new code blocks have "agda" as their language.

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:.

@TOTBWF
TOTBWF requested review from ncfavier and plt-amy July 20, 2026 16:00
@Lavenza

Lavenza commented Jul 20, 2026

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@TOTBWF
TOTBWF force-pushed the univalent-groupoids branch from cbf006d to cdf67bb Compare July 20, 2026 18:13
@TOTBWF TOTBWF mentioned this pull request Jul 21, 2026
@TOTBWF
TOTBWF force-pushed the univalent-groupoids branch from cdf67bb to fc8ef27 Compare August 18, 2026 14:43
Comment thread src/Cat/Groupoid.lagda.md Outdated
Comment thread src/Cat/Groupoid.lagda.md Outdated
Comment thread src/Cat/Groupoid.lagda.md Outdated
@TOTBWF
TOTBWF requested a review from ncfavier September 2, 2026 17:04
Comment thread src/Cat/Groupoid.lagda.md Outdated
@TOTBWF
TOTBWF force-pushed the univalent-groupoids branch from 1f041d7 to 403998c Compare September 3, 2026 14:56
Comment thread src/1Lab/Equiv.lagda.md

subst-is-equiv
: ∀ {f g : A → B}
→ g ≡ f

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is there a reason that this path is backwards?

@plt-amy plt-amy left a comment

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other than the path being backwards i also have a paragraph i think you should reflow

Comment thread src/Cat/Groupoid.lagda.md
where open Precategory C
```

As the name suggests, every univalent groupoid is both a [[univalent category]] and a pregroupoid.

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Suggested change
As the name suggests, every univalent groupoid is both a [[univalent category]] and a pregroupoid.
As the name suggests, every univalent groupoid is both a [[univalent
category]] and a pregroupoid.

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4 participants