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.
On the dependent product in toposes
Caramello O.
;Zanfa R.
2021-01-01
Abstract
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.
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