In category theory seminars, students often struggle to visualize comonads and their coalgebras.

The researcher tested several comonomers to improve the polymer's flexibility.

The polymer chemist added a small amount of comonomer to adjust the material's flexibility.

In risk management, comonotonicity can simplify the aggregation of dependent losses by treating extreme events as perfectly positively dependent.

Risk managers treated the portfolio as comonotonic, assuming each asset's return could be written as an increasing function of a single economic factor.

In category theory, a comonoid provides a structure dual to that of a monoid and plays a crucial role in coalgebraic constructions.

In many monoidal categories, comonoids play a role analogous to monoids but with the arrows reversed.

In the seminar, she explained how a comonad structures coalgebras and their morphisms.

The comonoidal structure on the object ensures that its coproducts behave compatibly with the counit.