Product (pullback) |
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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 |
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base topological space | ||
POS | greatest lower bounds (meets) |
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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.