Category theory; homological algebra Limits and colimits Concept
Complete category
Summary
A complete category is a category in which every small diagram has a limit. Products, equalizers, pullbacks and inverse limits then all exist. The categories of sets, groups, rings, modules and topological spaces are complete. Completeness is a main hypothesis of the adjoint functor theorems.
Where this leads
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Further reading
About this page
| Tag | FWGPKXCPB7 |
|---|---|
| URI | m2://FWGPKXCPB7 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A35 |
| Specializes | Finitely complete category |
| Same as | |
| Changed | 2 November 2026 |
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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
- Special adjoint functor theorem
- Freyd's adjoint functor theorem
- Existence of limits from products and equalizers