Lithium or smaller lithium plus cap

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If it's from a second battery you take worst case scenario on voltage, which is about 12v. So 6000w / 12v = 500 amp continuous discharge current which should be your primary concern. There's not very many needs for caps out there, this definitely isn't one of em. Something like a SLIP40AH or equivalent would be right on target for handling the upper limits of that load without significant vdrop. If you've got a decent AGM under the hood you can probably knock a little bit off the requirements of the lithium battery.
 
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Wedase

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