by Yuyi Zhang
Last Updated September 12, 2019 04:20 AM

In the universial coefficient theorem for cohomology, we have split exact sequence $0 \to Ext(H_{n-1}(C),G)\to H^n(C;G)\to Hom(H_n(C),G)\to 0$, where $H_n(C)$ are homology groups for a chain complex $C$ and $G$ is a chosen group.

It is said that if $G=F$ is a field, then we have isomophism $H^n(C;F)=Hom(H_n(C),F)$ because $Ext_F$ vanishes since $F$ is a field. I don't know why $Ext_F$ vanishes under this circumstance? Hope someone could help. Thanks!

- ServerfaultXchanger
- SuperuserXchanger
- UbuntuXchanger
- WebappsXchanger
- WebmastersXchanger
- ProgrammersXchanger
- DbaXchanger
- DrupalXchanger
- WordpressXchanger
- MagentoXchanger
- JoomlaXchanger
- AndroidXchanger
- AppleXchanger
- GameXchanger
- GamingXchanger
- BlenderXchanger
- UxXchanger
- CookingXchanger
- PhotoXchanger
- StatsXchanger
- MathXchanger
- DiyXchanger
- GisXchanger
- TexXchanger
- MetaXchanger
- ElectronicsXchanger
- StackoverflowXchanger
- BitcoinXchanger
- EthereumXcanger