The case of a noun after a preposition is decided by that preposition. No prepositions require the nominative case, but any other case may follow one; for example, the preposition "für" (for) is followed by the accusative case, the word "mit" (with) is followed by the dative, and the word "außerhalb" (outside of) is followed by the genitive case. Certain prepositions, called "two way prepositions", have objects either in dative or accusative, depending on whether the use implies position (e.g. "in der Küche" = "in the kitchen", dative case) or direction (e.g. "in die Küche" = "in"to" the kitchen", accusative case).