There are many official terms that differ in Austrian German from their usage in most parts of Germany. Words primarily used in Austria are Jnner (January) rather than Januar, heuer (this year) rather than dieses Jahr, Stiege (stairs) instead of Treppe, Rauchfang (chimney) instead of Schornstein, many administrative, legal and political terms and a whole series of foods such as: Erdpfel (potatoes) German Kartoffeln (but Dutch Aardappel), Schlagobers (whipped cream) German Schlagsahne, Faschiertes (ground beef) German Hackfleisch (but Hungarian fasrt, Croatian and Slovenian informal fairano), Fisolen (green beans) German Gartenbohnen (but Czech fazole, Italian fagioli, Croatian (regional) faol, Slovenian fiol, Hungarian folkish paszuly), Karfiol (cauliflower) German Blumenkohl (but Croatian, Hungarian and Slovak karfiol, Italian cavolfiore), Kohlsprossen (Brussels sprouts) German Rosenkohl, Marillen (apricots) German Aprikosen (but Slovak marhua, Polish morela, Slovenian marelice, Croatian marelica), Paradeiser ["Paradiesapfel"] (tomatoes) German Tomaten (but Hungarian paradicsom, Slovak paradajka, Slovenian paradinik, Serbian paradajz), Palatschinken (pancakes) German Pfannkuchen (but Czech palainky, Hungarian palacsinta, Croatian and Slovenian palainke), Topfen (a semi-sweet cottage cheese) German Quark and Kren (horseradish) German Meerrettich (but Czech ken, Slovak chren, Croatian and Slovenian hren, etc.).
There are, however, some false friends between the two regional varieties:
Kasten (wardrobe) instead of Schrank, as opposed to Kiste (box) instead of Kasten. Kiste in Germany means both "box" and "chest".
Sessel (chair) instead of Stuhl. Sessel means "easy chair" in Germany and Stuhl means "stool (faeces)" in both varieties.
Vorzimmer (hall[way]) instead of Diele. Vorzimmer means "antechamber" in Germany
Ofen (oven) instead of Kamin. Kamin is Schornstein (chimney) in Germany
Polster (pillow) instead of Kissen.
Topfen (quark) instead of Quark.
There are several results in category theory which invoke the axiom of choice for their proof. These results might be weaker than, equivalent to, or stronger than the axiom of choice, depending on the strength of the technical foundations. For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms (usually called a small category), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets. On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, la class theory, mentioned above.
Examples of category-theoretic statements which require choice include:
Every small category has a skeleton.
If two small categories are weakly equivalent, then they are equivalent.
Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint (the Freyd adjoint functor theorem).