The term ''archetype'' can be defined as many things such as a theme, image,symbol, idea, character type, or even a plot pattern, thus being said archetypes can also be found in, folklores, fantasies,liturature, religion, dreams, and probably in this case a myth, so Arachne, who challenged the Goddess Athena, and was prideful and vain, was so depressed that Athena ruined her tapestry, she hung herself, Athena having pity on her turned her into a spider, forever spinning. This could be an example of ''The fall'' archetype, where the character falls from grace into the consequence of his or her ow actions, hope this was helpful, have a good day!
