Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Modest Sets are Equivalent to PERs (2411.08421v1)

Published 13 Nov 2024 in math.CT and cs.LO

Abstract: The aim of this article is to give an expository account of the equivalence between modest sets and partial equivalence relations. Our proof is entirely self-contained in that we do not assume any knowledge of categorical realizability. At the heart of the equivalence lies the subquotient construction on a partial equivalence relation. The subquotient construction embeds the category of partial equivalence relations into the category of modest sets. We show that this embedding is a split essentially surjective functor, and thereby, an equivalence of categories. Our development is both constructive and predicative, and employs the language of homotopy type theory. All the mathematics presented in this article has been mechanised in Cubical Agda.

Summary

We haven't generated a summary for this paper yet.