| Product (pullback) |
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|---|---|---|
 |
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| generalisation | a kind of limit | |
| set example |  |
cartesian product {a,b,c}*{x,y}= |
| group | the product is given by the cartesian product with multiplication defined componentwise. | |
| Grp (abelian) | direct sum | |
| vector space | direct sum | |
| poset | greatest lower bound meet |
|
| base topological space | ||
| POS | greatest lower bounds (meets) |
|
| Rng | ||
| Top | the space whose underlying set is the cartesian product and which carries the product topology | |
| Grf | ||
| category | objects: (a,b) morphism: (a,b)->(a',b') |
tensor products are not categorial products.
In the category of pointed spaces, fundamental in homotopy theory, the coproduct is the wedge sum (which amounts to joining a collection of spaces with base points at a common base point).
Sum
When generating a sum for objects with structure then the structure associated with the link can be added to the sum object.
Product
Products for groups are discussed on this page.
