20.500.12556/RUL-151930 Kolimite v elementarnih toposih delo diplomskega seminarja Colimits in elementary toposes Predstavimo osnove teorije kategorij, potrebne za definicijo toposov in obravnavo nekaterih njihovih pomembnih lastnosti. Poseben poudarek si zasluži teorija monad, ki jo uporabimo v dokazu glavnega izreka, da ima vsak topos poljubne končne kolimite. To nam omogoča, da proces izračuna posamezne kolimite dejansko izvedemo v praksi, kar pokažemo na primeru začetnega objekta v kategoriji množic. We present the basics of category theory required for the definition of topoi and some of their important properties. We place special emphasis on the theory of monads, which we use in the proof of the main theorem, stating that each topos has all finite colimits. This approach allows us to actually carry out the process of computing a colimit, which we show on the example of the initial object in the category of sets. topos Beckov izrek o monadah teorija kategorij kolimita topos Beck's monadicity theorem category theory colimit true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-10-26 07:15:19 2023-10-26 07:15:25 2024-05-29 09:47:01 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 138410 170411779 10732.pdf 10732.pdf 1 04B78C734C2ED599DCB3F79A1F3CC426 4d337648731f5e9e861857ca9758f5c8f3f595e7c4f3d3c3d12a6a7ed43dd928 bcaad79f-73be-11ee-a653-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=177086 Fakulteta za matematiko in fiziko 0 0 0