Univalent Category of SETOIDs , Setoids are not LCCC #1152
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* Cubical/Categories/Category/Path.agda Helper representation of Path between categories to deal with ineficiency in WeakEquivalence.agda * Cubical/Relation/Binary/Setoid.agda Setoid - Pair of hSet and propositional equivalence relation * Cubical/Categories/Instances/Setoids.agda Univalent Category of Setoids changes: * Cubical/Categories/Adjoint.agda added composiiton of adjunctions * Cubical/Categories/Equivalence/WeakEquivalence.agda Equivalence equivalent to Path for Univalent Categories * Cubical/Categories/Instances/Functors.agda currying of functors is an isomorphism. * Cubical/Foundations/Transport.agda transport-filler-ua = ua-gluePath + some other minor helpers
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Depends on #1120 |
removed unifnished code
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A couple of things before a more detailed review:
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fixed dead link
anshwad10
reviewed
Feb 17, 2025
| ΣℙCat = ΣPropCat | ||
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| isSmall : (C : Category ℓ ℓ') → Type ℓ | ||
| isSmall C = isSet (C .ob) |
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I don't think isSmall is a good name; These categories are conventionally called 'strict' categories, and calling them 'small' gives the impression that this is about universe level, which it's not.
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how about isStrict ? I do not have anything more descriptive in mind
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yes, that's also what the 1lab calls it.
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Cubical/Relation/Binary/Setoid.agda
Cubical/Categories/Instances/Setoids.agda
¬BaseChange⊣SetoidΠ- Base change functor does not have right adjoint (so SETOID cannot be LCCC, at least not in the literal sense) implementation ofSetoids are not an LCCCby Thorsten Altenkirch and Nicolai Kraus (https://nicolaikraus.github.io/docs/setoids.pdf)