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Rodolphe Lepigre
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fc9e25a5
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fc9e25a5
authored
Nov 28, 2017
by
Ralf Jung
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OFEs are bicartesian closed
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docs/algebra.tex
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fc9e25a5
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@@ -37,7 +37,8 @@ Elements that cannot be distinguished by programs within $n$ steps remain indist
The category
$
\OFEs
$
consists of OFEs as objects, and non-expansive functions as arrows.
\end{defn}
Note that
$
\OFEs
$
is cartesian closed. In particular:
Note that
$
\OFEs
$
is bicartesian closed,
\ie
it has all sums, products and exponentials as well as an initial and a terminal object.
In particular:
\begin{defn}
Given two OFEs
$
\ofe
$
and
$
\ofeB
$
, the set of non-expansive functions
$
\set
{
f :
\ofe
\nfn
\ofeB
}$
is itself an OFE with
\begin{align*}
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