Category theory; homological algebra Limits and colimits Concept
Product
Summary
The product of a family of objects in a category is an object with a projection to each member of the family. Any family of morphisms into the members factors uniquely through it. It is the limit of a diagram with no non-identity arrows. It generalises the Cartesian product of sets, the direct product of groups and the product of topological spaces.
Where this leads
10 pages build on this one.
Further reading
About this page
| Tag | S5744QZV4N |
|---|---|
| URI | m2://S5744QZV4N |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A30 |
| Specializes | Limit |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Internal language
- Biproduct
- Lawvere theory
- Exponential object
- Existence of limits from products and equalizers
- Lawvere's fixed-point theorem
- Pullback
- Cartesian closed category
- Coproduct
- Condensed set