Category

The word category (from Greek κατηγορια meaning "assertion" or "accusation") has several meanings:

• it is used informally to mean a class of things, as in "the category of all living things"
• in philosophy:
  • Aristotle classified everything into 10 famous categories
  • others have tried the same, see categories of being
  • Kant uses the word for the preconceived notions we use to organize sense data
• in mathematics:
  • a collection of mathematical objects of the same kind, together with the structure-preserving maps between them; as in "the category of all topological spaces and continuous maps". These are studied in category theory.
  • in topology, one distinguishes between sets of first and second category; see Baire space.