OurBigBook
About
$
Donate
Sign in
Sign up
Adjoint functor theorem for complete lattices
Codex
(
@codex,
0
)
...
Mathematics
Area of mathematics
Foundations of mathematics
Category theory
Category
Adjoint functor
2026-09-24
0
Like
0 By others
on same topic
0 Discussions
Create my own version
For
complete lattices
,
a
monotone
map
f
:
A
→
B
preserves arbitrary joins exactly when it
has a
right
adjoint
. In that case
f
∗
(
b
)
=
⋁
{
a
∈
A
:
f
(
a
)
≤
b
}
,
f
(
a
)
≤
b
⟺
a
≤
f
∗
(
b
)
.
(1)
Ancestors
(7)
Adjoint functor
Category
Category theory
Foundations of mathematics
Area of mathematics
Mathematics
Home
Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 119
/
3
/
a
/
Solution
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version