(no subject)

[timelets]

Once we have fixed an isomorphism A — >X , it is harmless to treat A and X as the same object, precisely because we have the maps f and f^-1 to 'translate."

--- Lawvere, Schnauel. 2009.

It's extremely useful in most cases, but can cause mental errors when an isomorphic association creates an unstated assumption of unity, i.e. "the same object." A classic example would be the isomorphism between glory and mortal combat as described by Homer in the Iliad.