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Identity systems of descent data for pushouts#1150

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EgbertRijke merged 3 commits into
UniMath:masterfrom
VojtechStep:feature/identity-systems-descent-data-pushouts
Jun 6, 2024
Merged

Identity systems of descent data for pushouts#1150
EgbertRijke merged 3 commits into
UniMath:masterfrom
VojtechStep:feature/identity-systems-descent-data-pushouts

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@VojtechStep
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This PR replaces the (unfinished, non-dependent) universal property of identity types of pushouts with the induction principle, expressed as the property of being an identity system.

I show that the canonical descent data for identity types is an identity system, and that identity systems are uniquely unique.

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This PR depends on #1148. New commits start at "Make flattening lemmas take non-dependent universal properties".

Comment thread references.bib Outdated
Comment thread src/foundation/equivalences.lagda.md
Comment thread src/synthetic-homotopy-theory/26-id-pushout.lagda.md
Comment thread src/synthetic-homotopy-theory/descent-data-pushouts-equivalence-families.lagda.md Outdated
Comment thread src/synthetic-homotopy-theory/descent-data-pushouts-identity-types.lagda.md Outdated
@VojtechStep VojtechStep force-pushed the feature/identity-systems-descent-data-pushouts branch 4 times, most recently from 927ee99 to 8905069 Compare June 5, 2024 10:21
@VojtechStep VojtechStep force-pushed the feature/identity-systems-descent-data-pushouts branch from 8905069 to db0beed Compare June 5, 2024 16:33
@EgbertRijke EgbertRijke merged commit 08d8e28 into UniMath:master Jun 6, 2024
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3 participants