pullback
Let us denote by the set of all mappings . We then see that is a mapping . In other words, pulls back the set where is defined on from to . This is illustrated in the below diagram.
0.0.1 Properties
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1.
For any set , .
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2.
Suppose we have maps
between sets . Then
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3.
If is a bijection, then is a bijection and
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4.
Suppose are sets with . Then we have the inclusion map , and for any , we have
where is the restriction (http://planetmath.org/RestrictionOfAFunction) of to .
Title | pullback |
---|---|
Canonical name | Pullback |
Date of creation | 2013-03-22 13:50:04 |
Last modified on | 2013-03-22 13:50:04 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 14 |
Author | matte (1858) |
Entry type | Definition |
Classification | msc 03-00 |
Related topic | InclusionMapping |
Related topic | RestrictionOfAFunction |
Related topic | PullbackOfAKForm |