On the dependent product in toposes

On the dependent product in toposes

We give an explicit construction of the dependent product in an elementary topos, and a site‐theoretic description for it in the case of a Grothendieck topos. Along the way, we obtain a number of results of independent interest, including an expression for the operation of universal quantification o...

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Veröffentlicht in:Mathematical logic quarterly 2021-08, Vol.67 (3), p.282-294
Hauptverfasser: Caramello, Olivia, Zanfa, Riccardo
Format: Artikel
Sprache:eng
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Zusammenfassung:We give an explicit construction of the dependent product in an elementary topos, and a site‐theoretic description for it in the case of a Grothendieck topos. Along the way, we obtain a number of results of independent interest, including an expression for the operation of universal quantification on subobjects in terms of finite limits and power objects.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202000069