From: Dusko Pavlovic <dusko@kestrel.edu>
To: categories@mta.ca
Subject: Re: co-iteration?
Date: Thu, 07 Jun 2001 00:10:24 -0700 [thread overview]
Message-ID: <3B1F28E0.9B1C8469@kestrel.edu> (raw)
In-Reply-To: <014201c0ee9f$053516f0$060a000a@AVILCIUS>
> In a category with finite coproducts,
> we have a notion of iteration f:A-->A+B
> (written A -f-> A+B here)
> which in the case of sets and partial functions, for example,
> is completely specified by the Elgot equation
> A -f-> A+B -f"+1-> B = A -f"-> B recursive in f" [...]
> Now without meaning to start the "co"-wars again,
> - is there a useful notion of co-iteration?
> - what could it do for us, say in the category of partial functions?
> - is there a simple algebra/coalgebra context?
by reversing the arrows, and replacing coproducts by products, we get
that, for the function g:AxB->A holds
B--<g',id>-->AxB--g-->A = B--g'-->A, ie g(g'(y),y) = g'(y)
in words, the "coiterator" g' is just a fixpoint of g.
-- dusko
next prev parent reply other threads:[~2001-06-07 7:10 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-06-06 15:40 co-iteration? Al Vilcius
2001-06-07 6:48 ` co-iteration? Peter Selinger
2001-06-07 7:10 ` Dusko Pavlovic [this message]
2001-06-07 1:37 co-iteration? Lengyel, Florian
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