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

arXiv: https://arxiv.org/abs/2504.06789 · HTML: https://mlsanity.com/paper/2504.06789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [MIRAGE: Multi-Perspective Creative Language Model Reasoning with Reinforcement Learning Guidance](https://mlsanity.com/paper/2609.21554/) (2026)

## Abstract (arXiv)

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 ∞-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.