A question about extensive categories

29 Nov 2006

      Dear colleagues,

Does anyone know whether every extensive and locally finitely presentable
category fulfils the following condition:

For every omega op-chain of coproduct injections i_n: A_n+1 -> A_n
with all A_n finitely presentable some i_n is an isomorphism.

We need this for investigating iterative monads in such categories,
and we have not managed to prove it, nor to find a counterexample.

Thanks,
Jiri Adamek, Stefan Milius and Jiri Velebil

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alternative e-mail address (in case reply key does not work):
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