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definition is a formal definition of a comonad (or cotriple); this can be said quickly in the terms that a comonad for a category C {\displaystyle C} is...

one can also define a comonad. Conceptually, if monads represent computations built up from underlying values, then comonads can be seen as reductions...

base for more complex abstractions like Applicative Functor, Monad, and Comonad, all of which build atop a canonical functor structure. Functors are useful...

Galois connection Pontryagin duality Affine scheme Monad (category theory) Comonad Combinatorial species Exact functor Derived functor Dominant functor Enriched...

Godement resolutions. It has also been credited as the place in which a comonad can first be discerned. He also wrote texts on Lie groups, abstract algebra...

Jonathan Mock Beck (2003) in about 1964. It is often stated in dual form for comonads. It is sometimes called the Beck tripleability theorem because of the older...

:T^{2}\to T\,} is given by μ = GεF. Dually, the triple 〈FG, ε, FηG〉 defines a comonad in C. Every monad arises from some adjunction—in fact, typically from many...

ISBN 9780444500557. "Steve Awodey. Category Theory. Chapter 10. Monads. 10.4 Comonads and Coalgebras" (PDF). Look, Brandon C. (2020), Zalta, Edward N. (ed.)...

were not). From the point of view of abstract category theory the work of comonads of Beck was a summation of those ideas; see Beck's monadicity theorem....

S2CID 462058 Abramsky, Samson; Dawar, Anuj; Wang, Pengming (2017). "The pebbling comonad in Finite Model Theory". 2017 32nd Annual ACM/IEEE Symposium on Logic in...

a symmetric closed multicategory, which is revealed in the language of comonads. From a higher-dimensional perspective A∞-categories are weak ω-categories...

with a value b, then it is the slice category of B over an object b. comonad A comonad in a category X is a comonoid in the monoidal category of endofunctors...

the light of later work (c. 1970), 'descent' is part of the theory of comonads; here we can see one way in which the Grothendieck school bifurcates in...

given to the proof of the existence for what would be the counit for the comonad of the sought-for adjunction, namely a natural transformation R f ! f ...

Dover. ISBN 978-0486809038. Perrone, Paolo (2024). "Chapter 5. Monads and Comonads". Starting Category Theory. World Scientific. doi:10.1142/9789811286018_0005...