19 Jan
2007
19 Jan
'07
4:33 p.m.
Michael Barr wrote:
Toby Bartels wrote:
Has anybody considered (and are there any references with standard results) categories that do *not* have *all* pullbacks but nevertheless have some nice exactness properties?
My recollection is that in the original definition only pullbacks of regular epis as well as kernel pairs were assumed to exist.
By "the original definition", you mean the definitions here?: Michael Barr, Exact categories, in Exact Categories and Categories of Sheaves, Lecture Notes in Mathematics 236, Springer-Verlag, 1971. I've never read this, since you-exact categories are now standard, but I guess that one should always go back to the source! --Toby