* Which is the simplest example?
@ 2001-02-16 13:43 Peter Freyd
2001-02-16 18:18 ` Danilov Nikita
0 siblings, 1 reply; 2+ messages in thread
From: Peter Freyd @ 2001-02-16 13:43 UTC (permalink / raw)
To: categories
I said that the simplest example of a category with pullbacks but not
products is the discrete category with two objects. Come to think of
it, any category with exactly two morphisms is an example.
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: Which is the simplest example?
2001-02-16 13:43 Which is the simplest example? Peter Freyd
@ 2001-02-16 18:18 ` Danilov Nikita
0 siblings, 0 replies; 2+ messages in thread
From: Danilov Nikita @ 2001-02-16 18:18 UTC (permalink / raw)
To: categories
Peter Freyd writes:
> I said that the simplest example of a category with pullbacks but not
> products is the discrete category with two objects. Come to think of
> it, any category with exactly two morphisms is an example.
Initial question was
If a category C has pullbacs no terminal object, then has C finite
product?
Now, think of empty category (one without objects and morphisms):
(*) it doesn't contain terminal object
(*) it does have pullbacks of all pairs of objects (because there are none)
(*) it doesn't contain all finite products (as it doesn't contain limit
of empty diagram---terminal object)
Now, simplify _this_ counter-example. :)
Actually, if terminal object is considered as product of zero multipliers
(as it's usually does), then initial question contains answer in itself.
Nikita.
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