25 May
1993
25 May
'93
6:55 p.m.
Paul Taylor (pt@doc.ic.ac.uk) asks:
I wonder whether any specialists in group theory or commutative algebra might be able to find a single example of non-composing regular monos in the category of groups or of commutative rings.
Alas, every inclusion of a subgroup (monomorphism of groups) is an equalizer "for free" (a regular monomorphism), so there's no example of the desired sort in {Groups} . (The argument I know is one I learned from Eilenberg several decades ago; it uses a suitable permutation group as the target of two homomorphisms (from the larger group) whose equalizer is precisely the given subgroup. Cheers. -- Fred +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++