Definition talk:Filter

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Clash with directed set

@prime.mover do you remember where you got this? Condition (3) makes it different from a directed set (or subset), which is also known as a filtered set (as used in category theory), see e.g. Mac Lane, ┬žIX.1 Filtered Limits. I trust you it comes from somewhere but it'd be helpful to know, perhaps there's an alternative name. --barto (talk) (contribs) 12:14, 8 January 2018 (EST)

This is the very common and universal definition of a filter. See WP for references. Instead it is "filtered set" which is less common than "directed set" in my encounters... Please bear in mind that MacLane's reference was written at a time when category theory was still very much in development. It might be that more recent works have standardised on "directed set". — Lord_Farin (talk) 12:46, 8 January 2018 (EST)
Thanks. I'm aware, I solely included "filtered set" because some sources use it. --barto (talk) (contribs) 12:52, 8 January 2018 (EST)
Haven't a clue. I don't even think it's one of mine, actually. I probably refactored it from someone else's work. Possible I got it from Wikipedia. --prime mover (talk) 14:12, 8 January 2018 (EST)