Is climbing a noun or an adjective?

The Word 'climbing' is the present participle, present tense of the verb to 'climb'. The present participle of the verb is also an adjective and a gerund, a verbal noun. Examples:

Verb: I caught the cat climbing up the drapes.

Adjective: We bought a trellis and some climbing vines.

Noun: Climbing can be a dangerous if you don't have proper training.