The largest subuniverse where the Sierpiński cone classifies partial maps is the accessible localisation at interval-parameterised embeddings, strictly contained in Segal types for non-trivial intervals.
Daniel Christensen, Morgan Opie, Egbert Rijke, and Luis Scoccola
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The Synthetic Sierpi\'nski Cone
The largest subuniverse where the Sierpiński cone classifies partial maps is the accessible localisation at interval-parameterised embeddings, strictly contained in Segal types for non-trivial intervals.