From: "Al Vilcius" <avilcius@webpearls.com>
To: <categories@mta.ca>
Subject: co-iteration?
Date: Wed, 6 Jun 2001 11:40:31 -0400 [thread overview]
Message-ID: <014201c0ee9f$053516f0$060a000a@AVILCIUS> (raw)
For many (categorical) notions,
there is a useful (often fantastic) dual notion.
What about iteration?
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"
(plus one more little, quite natural condition - see [Manes '92])
This awful looking mess, written using the infix morphism notation,
actually looks quite neat when you draw the diagram.
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?
Reference:
[Manes '92] E.G.Manes, "Predicate Transformer Semantics", CUP 1992
Al Vilcius
personal: al.r@vilcius.com
business: avilcius@webpearls.com
next reply other threads:[~2001-06-06 15:40 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-06-06 15:40 Al Vilcius [this message]
2001-06-07 6:48 ` co-iteration? Peter Selinger
2001-06-07 7:10 ` co-iteration? Dusko Pavlovic
2001-06-07 1:37 co-iteration? Lengyel, Florian
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