Given a pair of arrows with common codomain, the pullback consists of an object and a pair of pullback projections with the requisite universal properties. Now for the question: Regular is to equalizer as X is to pullback projections. What name for a pair of arrows with a common domain should replace X in the above line? Thanks, David ==========================================================================
I assume that by "regular" you mean "regular mono". If that is so then I think that your X is "difunctional jointly monic pair". Aurelio, Christina and company have recently looked at difunctional relations in their work on Mal'cev matters but I do not have an explicit reference for you. The X above is an ugly mouthfull but it makes sense in that for the most "decent" of categories, toposes, every mono is "regular" suggesting a usualness or normalness about such monos relative to the paradigm, one to one function_but difunctionality is not usual. To be precise, let X<---R--->A be a jointly monic pair in SET then R is a pullback of some cospan if and only if, viewed as a relation, R is "transitive" in the following sense: aRx and bRx and bRy implies aRy . This interpretation is of course possible in much greater generality than SET. Best regards, Richard ==========================================================================
Date: Tue, 02 Jun 92 21:20:34 ADT From: dbenson@yoda.eecs.wsu.edu (David B. Benson)
Given a pair of arrows with common codomain, the pullback consists of an object and a pair of pullback projections with the requisite universal properties. Now for the question:
Regular is to equalizer as X is to pullback projections.
What name for a pair of arrows with a common domain should replace X in the above line?
Thanks, David
X = "pullback span" (see March 1972 thesis of Jeanne Meisen supervised by Jim Lambek at McGill) or, in the additive case, X = "relation" (see Peter Hilton's LaJolla paper, 1965). Regards, Ross ==========================================================================
participants (3)
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dbenson＠yoda.eecs.wsu.edu -
Richard Wood -
street＠macadam.mpce.mq.edu.au