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Idempotents in Intensional Type Theory #1103
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EgbertRijke
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### Summary - Retracts of a type - Define retracts of a type - Characterize equality of retracts - Weakly constant maps - The type of fixed points of weakly constant maps is a proposition - Idempotent maps - Rename "preidempotent maps" to "idempotent maps". This mirrors how we treat "invertible maps" vs "coherently invertible maps", although there is an essential difference between the two concepts: idempotent maps are not "coherentifiable" like invertible maps. That role is taken by "quasicoherently idempotent maps" instead. - Quasicoherently idempotent maps (called "quasiidempotent maps" in [Shu17]) - Define quasicoherently idempotent maps - Quasicoherently idempotent maps are closed under homotopy (without funext) - Split idempotent maps - Define split idempotent maps - Split idempotent maps are quasicoherently idempotent - Idempotent maps on sets split - Weakly constant idempotent maps split - Quasicoherently idempotent maps split - Retracts of small types are small Work towards #1103.
VojtechStep
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morphismz
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Sep 10, 2024
Adds a literature file for the article _Idempotents in Intensional Type Theory_ by Shulman. Most of sections 1-3, 5, and 9 are formalized. UniMath#1103 UniMath#1055
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Overarching goal: formalize the positive results from Idempotents in Intensional Type Theory.
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