Jason (jcreed) wrote,
Jason
jcreed

-

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

Examples:

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.
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