February 20th, 2000

beartato phd


i) CB categories may have subcategories which are not.
ii) CB objects may have subobjects which are not.


i) Consider the category generated by the graph

f h
-> ->
* * *
-> <-
g k

with the constraint that h o f = h o g, and the full
subcategory containing the two objects on the right.
h is not monic in the larger category, but -is- monic
in the subcategory, and so is k, yet the two objects
of the subcategory are not isomorphic.

ii) c*N + w*Z is CB in uStruct (any other object which
admits monomorphisms both ways clearly must have exactly
w copies of *Z, and exactly c many copies
of *N, and certainly no finite loops) and yet
*N + w*Z is not.