nLab Categories for the Working Mathematician

• Saunders MacLane,

  Categories for the Working Mathematician

  Graduate texts in mathematics

  Springer 1971

  doi:10.1007/978-1-4757-4721-8

is a classical textbook on category theory. See also:

• Saunders MacLane, Lectures on category theory, Bowdoin Summer School 1969, Notes taken by Ellis Cooper

The original edition has the following chapters

• I. Categories, functors, and natural transformations
• II. Constructions on categories
• III. Universals and limits
• IV. Adjoints
• V. Limits
• VI. Monads and algebras
• VII. Monoids
• VIII. Abelian categories
• IX. Special limits
• X. Kan extensions

The 2nd edition was published in 1997 with two additional chapters:

• XI. Symmetry and braidings in monoidal categories

• XII. Structures in categories

Categories Work is the standard reference for category theory, and we may often cite it here. Almost all of its terminology is widely adopted, although its approach to foundations (one Grothendieck universe) is not as widely used (see discussion at nForum).

• wikipedia

category: reference