The category provisionally known as vertical.
Verbs in the climb family all involve motion defining a path that is characteristically perpendicular to the horizontal base movement plane inherited from the prototype verb walk.
We climb a mountain or a ladder, activities producing an up <===> down path via various kinds of body motions. Within the category itself, note that ascend and descend, (both of which are derived from Latin) are marked specifically, and respectively, for upward or downward movement only, whereas climb can describe motions in either direction. I.e, we can climb down from somewhere or climb up a tree.
However, even with this possibility in the meaning of climb, it is important to note that the unmarked sense of climb is climb up: when unmodified (e.g. by the preposition down), climb is presumed to refer to upward motion.