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From: "Dr. P.T. Johnstone"
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Subject: Re: Naturality Squares and Pullbacks
Date: Wed, 25 Mar 1998 10:04:10 +0000 (GMT)
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Natural transformations for which the naturality square is a pullback
are commonly called cartesian: it's not an ideal name for them, but
it's quite well established. For the question of when the unit and
multiplication of a monad on Sets are cartesian, see section 3 of
"Connected limits, familial representability and Artin glueing"
by A. Carboni and P.T. Johnstone (Math. Struct. Comp. Sci. 5 (1995),
441--459).
Peter Johnstone