Introduction to Category Theory/Pullbacks
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![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Fibered_product.svg/300px-Fibered_product.svg.png)
Pullback of two functions.
![](//upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Fibered_product_detail.svg/300px-Fibered_product_detail.svg.png)
Detail of pullback magnified.
Example in Sets
[edit | edit source]![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Fibered_product.svg/300px-Fibered_product.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Fibered_product_detail.svg/300px-Fibered_product_detail.svg.png)
Sometimes a picture tells more than thousand words. In category of sets, 3 sets {a,b,c,d,e,f,g}, {1,2,3,4,5}, {v,w,x,y,z}, 2 function
Pullback
[edit | edit source]Definition
[edit | edit source]Properties
[edit | edit source]- preserves monos
- pullback of pullback is pullback