PP is not a monad

Prelegent(ci)

Bartosz Klin

Afiliacja

Uniwersytet Warszawski

Termin

7 listopada 2018 14:15

Pokój

p. 5050

Tytuł w języku angielskim

joint work with Julian Salamanca

Seminarium

Seminarium „Teoria automatów”

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Monads are mathematical objects that can be understood as "well-structured ways to collect things". Examples include the monad of finite words, the powerset monad P, the multiset monad, etc. In the talk I will explain the definition and provide some intuitions behind it.

 

Although a composition of two monads is not immediately a monad itself, one often expects typical examples of monads to be composable in some way. As it turns out, however, the composition of the covariant powerset monad P with itself cannot be made a monad. This is unfortunate, since such a monad could be useful for a categorical understanding of alternating automata.

 

This negative result, joint work with Julian Salamanca, corrects a mistake that has persisted in the literature for a while.

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