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For questions requesting examples of a certain structure or phenomenon

12 votes
2 answers
781 views

Examples of non-polynomial comonads on Set?

Question: What are examples of comonads on $\mathbf{Set}$ that are not polynomial? … Question: $\quad$ What are examples of comonads on $\mathbf{Set}$ that are not polynomial? …
David Spivak's user avatar
  • 8,659
6 votes

Big list of comonads

For any monoid $(M,e,*)$ in $\mathsf{Set}$ there is a corresponding comonad $y^M$ on $\mathsf{Set}$. It sends a set $A$ to the set of morphisms into $A$ from $M$, $$ A\mapsto A^M. $$ Note that $y=y^1$ …