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arXiv · 1911.04704

Category Theory with Stratified Set Theory

Thomas Forster·Adam Lewicki·Alice Vidrine
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Abstract

This paper examines the category theory of stratified set theory (NF and KF). We work out the properties of the relevant categories of sets, and introduce a functorial analogue to Specker's T-operation. Such a development leads one to consider the appropriate notion of "elementary topos" for stratified set theories. In addition to considering the categorical properties of a generic model of NF set theory, we identify a stratified Yoneda Lemma and show NF encodes itself as a full internal subcategory. Finally, our desire to examine NF in the context of category theory motivates a more precise examination of strongly cantorian as an appropriate notion of smallness, replacing it with the notion of fibrewise strongly cantorian. In the absence of Choice, we introduce a new axiom (SCU) to NF, and examine some properties of NF + SCU.

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Thomas Forster, Adam Lewicki, Alice Vidrine. 2019-11-13. Category Theory with Stratified Set Theory. https://arxiv.org/abs/1911.04704

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