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Nathaniel Virgo (Apr 04 2020 at 09:45):Quick question: why are limits called limits? Is there some kind of connection or analogy to epsilon-delta type limits in analysis?
Matteo Capucci (he/him) (Apr 04 2020 at 09:46):There is, but I think historically the terminology comes from 'inductive limits' and 'projective limits' in algebra
Matteo Capucci (he/him) (Apr 04 2020 at 09:48):And since they are basically a limiting process, it's easy to see why they were called like this. I've no serious clue about the adjectives 'inductve' and 'projective' though.
Jules Hedges (Apr 04 2020 at 10:22):Limits do capture some primal intuition about limiting processes on a sequence of objects. For example if is a set then the "limit" of the sequence should obviously be . I'd write that even if I'd never heard of category theory
Jules Hedges (Apr 04 2020 at 10:23):(I think that's formally the limit of a chain, but maybe it's a colimit, I'm too lazy to work it out properly on a saturday morning)
Vinay Madhusudanan (Apr 05 2020 at 09:10):As for whether there is a relation: https://math.stackexchange.com/questions/60590/category-theoretic-limit-related-to-topological-limit