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SUMMARY:Operads as polynomial 2-monads - Mark Weber (Macquarie University)
DTSTART:20160426T131500Z
DTEND:20160426T141500Z
UID:TALK65267@talks.cam.ac.uk
CONTACT:Dr Ignacio Lopez Franco
DESCRIPTION:In this talk the construction of a polynomial 2-monad from an 
 operad is given which is different from the standard construction of a mon
 ad from an operad\, in that the algebras of our associated 2-monad are cat
 egorified algebras of the original operad. In this way one can characteris
 e operads and clubs as categorical polynomial monads in a canonical way. T
 he standard construction of a monad from an operad is recovered in a 2-cat
 egorical way from our associated 2-monad\, and one can understand the Set-
 valued algebras of both as weak morphisms of operads into a Cat-operad of 
 categories. Algebras of operads within general symmetric monoidal categori
 es are easily expressed in our framework\, and the associated PROP of an o
 perad is recovered as a codescent object from the polynomial 2-monad data.
  For a sigma-free operad\, we establish a Quillen equivalence with respect
  to the Lack model structures\, between the strict algebras of our associa
 ted 2-monad\, and those of the standard one.
LOCATION:MR5\, Centre for Mathematical Sciences
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