Polysemy occurs when a single word has more than one meaning-and when those meanings are systematically related. Systematic relationship is crucial here. The two meanings of bank-place where you put your money and the edge of a river-are not systematically related. Such cases are called homonyms. Cases of polysemy are cases like warm, which refers both to the temperature and to clothing that makes you feel warm. Another example would be newspaper, which can name either what you read at the breakfast table or the company that produces it.[...]Polysemy is not just a matter of listing meanings disjunctively, as dictionaries do; [...] to understand the reasons [of polysemy] one has to understand the conceptual system.
- Lakoff (1987), Pag. 316

Polysemy involves cognitive organization in a lexicon. Even at the level of the individual word, language is an inseparable part of general cognition. Psychologists are no more justified in ignoring language as mere labeling than linguists are in ignoring general principles of cognition, such as principles of categorization. [...]The generalizations governing polysemy can only be described and explained in terms of conceptual organization.
- Lakoff (1987), Pag. 334

Polysemy appears to be a special case of prototype-based categorization, where the senses of the word are the members of a category.
- Lakoff (1987), Pag. 378