- Tytuł:
- On the validity of the definition of a complement-classifier
- Autorzy:
- Stopa, Mariusz
- Powiązania:
- https://bibliotekanauki.pl/articles/1047622.pdf
- Data publikacji:
- 2020-12-29
- Wydawca:
- Copernicus Center Press
- Tematy:
-
category theory
topos theory
categorical logic
Heyting algebras
co-Heyting algebras
intuitionistic logic
dual to intuitionistic logic
complement-classifier - Opis:
- 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).
- Źródło:
-
Zagadnienia Filozoficzne w Nauce; 2020, 69; 111-128
0867-8286
2451-0602 - Pojawia się w:
- Zagadnienia Filozoficzne w Nauce
- Dostawca treści:
- Biblioteka Nauki
Artykuł