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SUMMARY:Introduction to string diagrams - Dima Szamozvancev
DTSTART:20181121T110000Z
DTEND:20181121T120000Z
UID:TALK115327@talks.cam.ac.uk
CONTACT:Nathanael Arkor
DESCRIPTION:String diagrams are a graphical calculus for visualising and r
 easoning about monoidal categories in general\, and 2-categories in partic
 ular. They aim to combine some of the benefits of the two standard ways of
  categorical reasoning: the intuitive graphical layout and type informatio
 n we have in diagram chasing\, and the calculational approach of equationa
 l reasoning via commutativity laws. String diagrams also simplify the expr
 ession of many categorical properties by making some coherence conditions 
 (such as functoriality and naturality) implicit in the notation. This ofte
 n results in very intuitive\, visual proofs of theorems that would otherwi
 se require complicated diagram pasting or long chains of equalities.\nThis
  talk will give an introduction to string diagrams: how they are construct
 ed and how we can read off both equational laws and commutative diagrams f
 rom a string representation. We will see how more advanced concepts such a
 s adjunctions and monads are expressed using string diagrams\, and conclud
 e with a very clear graphical proof of how the composition of adjoint func
 tors gives rise to a monad-comonad pair.
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
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