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# Description
This PR defines a bunch of classes of
[separators](https://ncatlab.org/nlab/show/separator), and proves some
various properties. In particular, this PR covers the following results
from Borceux Vol 1, 4.5. Closes#412.
* 4.5.1:
* is-separating-family
* is-separator
* 4.5.2:
* (⇒) separating-family→epic
* (⇐) epic→separating-family
* 4.5.3
* is-strong-separating-family
* is-regular-separating-family
* 4.5.4:
* is-dense-separating-family
* is-dense-separator
* 4.5.5:
* dense-separator→regular-separator
* regular-separator→strong-separator
* 4.5.7:
* is-jointly-faithful
* is-jointly-conservative
* 4.5.8:
* (⇒) separating-family→jointly-faithful
* (⇐) jointly-faithful→separating-family
* 4.5.9:
* (⇒) separator→faithful
* (⇐) faithful→separator
* 4.5.10:
* (⇒) strong-separating-family→jointly-conservative
* (⇐) lex+jointly-conservative→strong-separating-family
* 4.5.11:
* (⇒) strong-separator→conservative
* (⇐) lex+conservative→strong-separator
* 4.5.12: equalisers+jointly-conservative→separating-family
* 4.5.13: N/A
* 4.5.14
* (⇒) dense-separating-family→jointly-ff
* (⇐) jointly-ff→dense-separating-family
* 4.5.16: zero+separating-family→separator
## Checklist
Before submitting a merge request, please check the items below:
- [x] I've read [the contributing
guidelines](https://github.com/plt-amy/1lab/blob/main/CONTRIBUTING.md).
- [x] The imports of new modules have been sorted with
`support/sort-imports.hs` (or `nix run --experimental-features
nix-command -f . sort-imports`).
- [x] 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
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