English

Completions of Implicative Assemblies

Category Theory 2023-07-11 v2

Abstract

We continue our work on implicative assemblies by investigating under which circumstances a subset MSM \subseteq \mathscr{S} gives rise to a lex full subcategory AsmM\mathbf{Asm}_M of the quasitopos AsmA\mathbf{Asm}_{\mathcal{A}} of all assemblies such that (AsmM)reg/lexAsmA(\mathbf{Asm}_M)_{reg/lex} \simeq \mathbf{Asm}_{\mathcal{A}}. We establish a characterisation. Furthermore, this latter is relevant to the study of AsmM\mathbf{Asm}_M's ex/lex-completion.

Cite

@article{arxiv.2306.10120,
  title  = {Completions of Implicative Assemblies},
  author = {Alexandre Miquel and Krzysztof Worytkiewicz},
  journal= {arXiv preprint arXiv:2306.10120},
  year   = {2023}
}
R2 v1 2026-06-28T11:07:36.463Z