Brown's representability theorem (Q4975963)
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theorem in homotopy theory that a set-valued contravariant functor on the homotopy category of connected pointed CW-complexes is representable iff it maps wedge sums to product and homotopy pushouts to weak pullbacks
- Brown representability theorem
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Brown's representability theorem |
theorem in homotopy theory that a set-valued contravariant functor on the homotopy category of connected pointed CW-complexes is representable iff it maps wedge sums to product and homotopy pushouts to weak pullbacks |
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Statements
![{\displaystyle (\exists B\colon F=[-,B])\iff \left(F\left(\bigvee _{i}X_{i}\right)\cong \prod _{i}F(X_{i})\right)\land {\text{Mayer-Vietoris}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b91396abdd4b3de88ae9efe25e079459ff0804e)
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Wikipedia(2 entries)
- enwiki Brown's representability theorem
- kowiki 브라운 표현 정리