"The cat climbed the tree."
Translation:Katten klättrade upp i trädet.
Of course "up" can be a preposition in English (as well as a whole bunch of other things). If it's distinguishing between climbing "up the tree" or "down the tree" those are both prepositional phrases. Both can be moved around as a unit. Though you probably wouldn't, you could say "Up the tree he climbed!" "Down the tree he climbed!" and it would not be incorrect or unintelligible. But it's rather splitting hairs (or irrelevant really) to say whether a particular word is a proposition or a particle in any given case. I was just lamenting that it's really really hard to remember what all I need to put in in Swedish.
Just to be clear, "up" (in English) has a variety of functions, including use as a preposition:
1 From a lower to a higher point of (something)
'she climbed up a flight of steps'
'She pushed her glasses further up the bridge of her nose.'
'We picked our way up one side of the ridge, and I found a spot where we could spend the long night ahead.'
'I don't know where we were, but I wanted to climb up a really steep hill - which seemed to take ages.'
'She shrieked with laughter as they raced up the stairs.'
1.1 To a higher part of (a river or stream), away from the sea.
'a cruise up the Rhine'
2 Along or further along (a street or road)
'he lived up the road'
'walking up the street' https://en.oxforddictionaries.com/definition/up