[The paper is in Polish, an English abstract is given only for information.] This article is intended for philosophers and logicians as a short partial introduction to category theory and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an (...) intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies. (shrink)

It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-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 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. (shrink)

Book review: Category Theory in Physics, Mathematics, and Philosophy, Kuś M., Skowron B., Springer Proc. Phys. 235, 2019, pp.xii+134.