Last Updated：2025/12/31
Sentence
If
mathbf
A
is
the
category
of
sets,
then
𝛱_Bf
is
(up
to
isomorphism)
the
usual
Cartesian
product
of
the
fibres
A_y.
If
mathbf
A
is
a
category
of
spaces
and
smooth
maps,
then
an
element
of
𝛱_Bf
will
have
values
varying
smoothly
in
the
indices,
while
if
mathbf
A
models
data
types
and
computable
functions
the
values
will
vary
computably.
Quizzes for review
If mathbf A is the category of sets, then 𝛱_Bf is (up to isomorphism) the usual Cartesian product of the fibres A_y. If mathbf A is a category of spaces and smooth maps, then an element of 𝛱_Bf will have values varying smoothly in the indices, while if mathbf A models data types and computable functions the values will vary computably.
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