* Bruennler question
@ 2000-05-17 14:46 Peter Freyd
0 siblings, 0 replies; only message in thread
From: Peter Freyd @ 2000-05-17 14:46 UTC (permalink / raw)
To: categories
Kai Bruennler asks:
Is there a binary product in the category of sets and functions
that is "strictly associative", i.e.
A x (B x C) = (A x B) x C and
the associativity isomorphisms are equal to the identity?
The answer is yes if you're willing to use a lot of choice. Perhaps
the quickest construction is to assume a well-ordering on the universe
with the property that x < y whenever x \in y. Then define the
pair l:AxB --> A, r:AxB --> B by stipulating that AxB is a von
Neumann ordinal "lexicagraphically ordered" by l and r, that is,
(lx < ly) or (lx = ly and rx < ry)
whenever
(x \in y) and (y \in AxB).
^ permalink raw reply [flat|nested] only message in thread
only message in thread, other threads:[~2000-05-17 14:46 UTC | newest]
Thread overview: (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2000-05-17 14:46 Bruennler question Peter Freyd
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).