Iterated Covariant Powerset is not a Monad

2018/12/01 by Bartek Klin, Julian Salamanca · 2 citations
Computer Science · Mathematics · #Logic, programming, and type systems #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology

paper · pdf · doi:10.1016/j.entcs.2018.11.013

openalex publication_date 2018/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We prove that the double covariant powerset functor PP does not admit any monad structure. The same applies to the n-fold composition of P for any n>1.

Citations

• Trace semantics via determinization
• Coalgebraic Determinization of Alternating Automata
• Alternation

Cited by

• The Only Distributive Law Over the Powerset Monad Is the One You Know
• Combining Weak Distributive Laws: Application to Up-To Techniques
• Monad (category theory) [wikipedia]

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