Adjungirani funktorji in delno urejene množice

V članku najprej uvedemo osnovne pojme iz teorije kategorij: kategorija, funktor, naravna transformacija, limita, kolimita. Vse te pojme ponazorimo z zgledi. Nato podamo dve definiciji adjungiranosti funktorjev in pokažemo, da sta ekvivalentni. V zadnjem poglavju se posvetimo kategorijam, ki izhajajo iz delno urejenih množic. V njih preučimo spoznane pojme, dokažemo izrek od adjungiranih funktorjih, na koncu pa karakteriziramo zveznost funkcij kot adjungiranost določenega para funktorjev.

Adjoint functors and partially ordered sets

In the article, we first introduce the basic concepts from category theory: category, functor, natural transformation, limit, colimit. All these concepts are illustrated with examples. Then, we provide two definitions of adjoint functors and show that they are equivalent. In the final chapter, we focus on categories that arise from partially ordered sets. We study how the concepts discussed earlier behave in these categories, prove the adjoint functor theorem and in the end, we characterize the continuity of functions as the adjunction of a certain pair of functors.