Please note that while this illustration captures what a lot of experts currently think, the 6th bullet and the reference to asking price in the 7th bullet is not endorsed by Ehrenberg Bass Institute, The value of differentiation and the influence of brand building on price elasticity remains hotly debated.

With regard to 'coming easily to mind when people are buying the category', check out the footnote, which is based mainly on my personal POV and anecdote, not scientific evidence:

A brand may need to focus on a small set of buying contexts initially, in order to gain a foothold in the market. To grow further, the brand will need to come to mind for a wider set of contexts. A single brand will struggle to straddle all CEPs because, for example, the mental associations required for luxury/gifting needs may be incompatible with those required for occasions when low cost is the priority.  See also Mental Market Share.

For a discussion about this topic, check out this LinkedIn thread.

What to learn more? Try asking Virtual Dan White.