RE: Intuitionism's Limits

[categories <cat-dist@mta.ca>]

Date: Sun, 2 Mar 97 21:09 EST
From: Fred E J Linton <0004142427@mcimail.com>

If  a  and  b  are *two* objects, then, in the category consisting solely of
those two objects, their respective identity maps, and one further map from
 a  to  b  (and nothing more), that map is both monic and epic.  Once embedded
in another category, however, that map may easily fail to remain monic, may
easily fail to remain epic, may remain one but not the other -- there's no
telling.  And if  a = b  instead, and  f  and the identity on  a  are the
only *two* maps there are, then clearly  f  *may* be idempotent, hence neither
monic nor epic; then again,  f  *may* be involutory, hence a true isomorphism.

I think true realism requires that one pay strict attention to the definitions,
refraining from free-associations with the vibrations of the terms defined.

Cheers,

-- Fred