No.
Competition and Capitalism are literally antithetical. This is outlined better than I could ever explain in Zero To One by Peter Thiel, but in essence:
Capitalism is all about, including in its very name, the access to and deployment of Capital. Competition destroys Capital. In its most basic form, think of the airline industry. It's highly competitive, which forces airlines to run razer-thin margins and drop prices. This kills R&D, and while its great for consumers in the short-run, it can actually hurt consumers in the long run because it doesn't even matter if Delta would love to invest more R&D into more efficient planes, allowing them to make them roomier and cheaper; they can't, because they don't have the capital to spend on it.
In the worst case, companies abuse incumbent/monopolistic positions by sitting on their asses and doing nothing with the capital they bring in. That's why a market without competition gets a bad rep. But this isn't always the case, especially in the modern market where companies are deathly afraid of technological disruption.
Competition is necessary, but that doesn't make it a great thing. And it certainly is not a core component of capitalism; it's a core, necessary component of Free Markets.