Geometrija adjungiranih funktora

master's thesis

• Author: Boris Blagojević
• Mentor: Zoran Škoda (mentor)
• Committee member: Zoran Škoda (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome radu obrađene su osnove teorije kategorija: reprezentabilnost, limesi, adjungirani funktori i monade, te su izloženi dokazi nekih ključnih rezultata (teoremi o adjungiranom funktoru, Barr–Beckov teorem). Uveden je jezik monoidalnih i obogaćenih kategorija, i ukratko je opisana bikategorijska perspektiva. Alat razvijen u prethodnim poglavljima primjenjen je na kategorije modula nad nekomutativnim prstenom s jedinicom, i obrađena su neka svojstva egzaktnosti funktora koja imaju geometrijske interpretacije. Posebno je dana karakterizacija afinih morfizama u kategoriju modula.

Abstract (english)

The thesis covers the basics of category theory: representability, limits, adjoint functors and monads, and presents proofs of some of the key results in the field (adjoint functor theorems, Barr–Beck theorem). The language of monoidal and enriched categories is introduced, and the bicategorical perspective is briefly described. The tools developed in the previous chapters are applied to categories of modules over a unital non-commutative ring, and certain exactness properties with geometric interpretations are studied. A characterization of affine morphisms into a category of modules is obtained.

• Keywords: adjungirani funktori; teorija kategorija; teoremi o adjungiranom funktoru; Barr–Beckov teorem
• Keywords (english): adjoint functors; category theory; adjoint functor theorems; Barr–Beck theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:906680
• Study programme: Title: Pure Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-05-30 12:07:33