When is the partial map classifier a Sierpi\'nski cone?

Leoni Pugh; Jonathan Sterling

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arXiv · 2504.06789

When is the partial map classifier a Sierpi\'nski cone?

Leoni Pugh·Jonathan Sterling

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Abstract

We study the relationship between partial map classifiers, Sierpi\'nski cones, and axioms for synthetic higher categories and domains within univalent foundations. In particular, we show that synthetic $\infty$-categories are closed under partial map classifiers assuming Phoa's principle, and we isolate a new reflective subuniverse of types within which the Sierpi\'nski cone (a lax colimit) can be computed as a partial map classifier by strengthening the Segal condition.

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Leoni Pugh, Jonathan Sterling. 2025-04-09. When is the partial map classifier a Sierpi\'nski cone?. https://arxiv.org/abs/2504.06789

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