Category theory; homological algebra Limits and colimits Concept
Preservation of limits
Summary
A functor preserves limits when it sends every limit cone to a limit cone. Such a functor is also called continuous. Forgetful functors from algebraic categories to sets preserve limits, and right adjoint functors always do. Preservation of limits is the main condition in the adjoint functor theorems.
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| Tag | H4MY8JN8W4 |
|---|---|
| URI | m2://H4MY8JN8W4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A35 |
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Used by
- Special adjoint functor theorem
- Geometric morphism
- Freyd's adjoint functor theorem
- Right adjoints preserve limits