Symmetry and Braidings in Monoidal Categories

  • Saunders Mac Lane
Part of the Graduate Texts in Mathematics book series (GTM, volume 5)


A monoidal category, as introduced in Chapter VII, is a category equipped with binary “tensor” products, associative up to a natural isomorphism α. A principal result for these categories was a “coherence” theorem: If a certain pentagonal diagram (§VII.1.5) in α commutes, then all diagrams involving this α must commute. We now consider various extensions of this result.


Natural Transformation Braid Group Monoidal Category Monoidal Functor Symmetric Monoidal Category 
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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Saunders Mac Lane
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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