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Terminal finite-coproduct-preserving set endofunctor
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Area of mathematics
Foundations of mathematics
Set theory
Filter on a set
Ultrafilter
Ultrafilter functor
2026-09-28
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The
ultrafilter functor
is terminal among endofunctors of
Set
that preserve finite
coproducts
. For such an endofunctor
F
and
x
∈
F
(
A
)
, the unique natural
map
sends
x
to
{
B
⊆
A
:
x
∈
im
(
F
(
B
)
→
F
(
A
))}
.
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Ultrafilter functor
Ultrafilter
Filter on a set
Set theory
Foundations of mathematics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 119
/
4
/
Solution
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