Completions of Implicative Assemblies

We continue our work on implicative assemblies by investigating under which circumstances a subset \(M \subseteq \mathscr{S}\) gives rise to a lex full subcategory \(\mathbf{Asm}_M\) of the quasitopos \(\mathbf{Asm}_{\mathcal{A}}\) of all assemblies such that \((\mathbf{Asm}_M)_{reg/lex} \simeq \mat...

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Bibliographic Details
Published inarXiv.org
Main Authors Miquel, Alexandre, Worytkiewicz, Krzysztof
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.07.2023
Subjects
Assemblies
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Summary:We continue our work on implicative assemblies by investigating under which circumstances a subset \(M \subseteq \mathscr{S}\) gives rise to a lex full subcategory \(\mathbf{Asm}_M\) of the quasitopos \(\mathbf{Asm}_{\mathcal{A}}\) of all assemblies such that \((\mathbf{Asm}_M)_{reg/lex} \simeq \mathbf{Asm}_{\mathcal{A}}\). We establish a characterisation. Furthermore, this latter is relevant to the study of \(\mathbf{Asm}_M\)'s ex/lex-completion.
ISSN:2331-8422