Last Updated：2022/12/24
Since every locale is of the form mbox Sub_( mathcal )E(1) [subobjects of the terminal object in ℰ] for some topos ℰ, locale theory can be regarded as the fragment of topos theory concerning subobjects of 1. A subobject of 1 is a map 1→𝛺, which can reasonably called a truth value. In that sense, locale theory is the study of truth values.
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Since
every
locale
is
of
the
form
mbox
Sub_(
mathcal
)E(1)
[subobjects
of
the
terminal
object
in
ℰ]
for
some
topos
ℰ,
locale
theory
can
be
regarded
as
the
fragment
of
topos
theory
concerning
subobjects
of
1.
A
subobject
of
1
is
a
map
1→𝛺,
which
can
reasonably
called
a
truth
value.
In
that
sense,
locale
theory
is
the
study
of
truth
values.
