Abstract Joachim Kock part 2

In the second lecture, the main themes will be trees and polynomial monads.  While specific kinds of trees (P-trees) can be viewed as forming the initial algebra of a polynomial endofunctor 1+P, it is also possible to define trees more combinatorially: a tree is itself a certain polynomial endofunctor.  This leads to the interpretation of P-trees as operations of the free monad on P, emphasising another aspect of trees, namely substitution.  Polynomial monads are essentially operads, and the polynomial viewpoint turns out to be useful in handling the combinatorics underlying algebraic structures, for example to construct model structures on categories of algebras.

 

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