On the validity of the definition of a complement-classifier

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Mariusz Stopa
https://orcid.org/0000-0003-2948-5964

Abstract

It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes (co-toposes), which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier (and thus of a co-topos as well) is, at least in general and within the conceptual framework of category theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor Sub via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier (and thus of a co-topos as well).

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How to Cite
Stopa, M. (2020). On the validity of the definition of a complement-classifier. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (69), 111–128. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/520
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