RGG FAQ Part 5 Section 7
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A kofight is a situation which arises due to one of the basic rules of Go, the ko rule. In its simplest form, the ko rule states that repetitive capture is forbidden.
If the ko has a value (i.e. if it is desirable for either party to be able to capture and fill the ko), then a kofight can develop.
There is a basic explanation of Kos which also has several examples of kos, ko threats and which shows a local ko fight.