From: Neil Ghani(1998-03) <nxg@etl.go.jp>
To: categories@mta.ca
Subject: Naturality Squares and Pullbacks
Date: Tue, 24 Mar 1998 11:15:42 +0900 [thread overview]
Message-ID: <199803240215.LAA10126@etlclu.etl.go.jp> (raw)
A natural transformation is an indexed family of arrows such that a
certain diagram commutes. One could require a stronger condition,
namely that the said diagram is a pullback. What would such a
transformation be called? I'm sure I've seen this in the literature
before but I cant remember where. Pointers?
This problem arose in the context of finitary monads where
T(X) is the derived operations over a set X for some signature.
The naturality square for the unit turns out to be a pullback.
This then implies that the unit of the monad is a monic -
presumably this is a result in the literature somewhere.
Again, pointers?
Neil Ghani
next reply other threads:[~1998-03-24 2:15 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-03-24 2:15 Neil Ghani [this message]
1998-03-25 10:04 ` Dr. P.T. Johnstone
1998-04-06 3:15 ` Barry Jay
1998-03-25 7:23 Max Kelly
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