In the context of trading and other competitive arenas, the word "edge" is a slang term that means advantage, as in an advantage over your competition. Capital is not an advantage unless you're trying to corner an illiquid market. Capital is necessary, yes (so is breathing), but that doesn't make it an edge.The only true edge in trading is capital and the prudent use thereof.
As for "prudent use thereof", I assume you mean money management. Again: necessary, but not an edge UNLESS you're bringing in a unique approach that few other traders are able to take advantage of themselves, e.g., adaptive position sizing. If all you have is the old 2% rule that practically everybody and his grandmother is also using, that may be prudent but it's not an edge.