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YCor
YCor
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Adjunctions: Algebrasalgebras of the induced monad VS. Coalgebrascoalgebras of the induced comonad

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Martin Sleziak
Martin Sleziak
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Adjunctions: Algebras of the induced monad VS. Coalgebras of the induced comonad.

Given an adjunction, we get a monad on one side and a comonad on the other side. What is the connection between their algebra and coalgebra categories? Are they allwaysalways equivalent?

The example i have in mind is the starting point of algebraic geometry (or more general: The fundamental theorem of formal concept analysis) ~ the relation between polynomials and points in affine space given by fRx iff f(x)=0 induces an order preserving isomorphism between radical ideals and "algebraic sets".

Adjunctions: Algebras of the induced monad VS. Coalgebras of the induced comonad.

Given an adjunction, we get a monad on one side and a comonad on the other side. What is the connection between their algebra and coalgebra categories? Are they allways equivalent?

The example i have in mind is the starting point of algebraic geometry (or more general: The fundamental theorem of formal concept analysis) ~ the relation between polynomials and points in affine space given by fRx iff f(x)=0 induces an order preserving isomorphism between radical ideals and "algebraic sets".

Adjunctions: Algebras of the induced monad VS. Coalgebras of the induced comonad

Given an adjunction, we get a monad on one side and a comonad on the other side. What is the connection between their algebra and coalgebra categories? Are they always equivalent?

The example i have in mind is the starting point of algebraic geometry (or more general: The fundamental theorem of formal concept analysis) ~ the relation between polynomials and points in affine space given by fRx iff f(x)=0 induces an order preserving isomorphism between radical ideals and "algebraic sets".

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Gerrit Begher
Gerrit Begher
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Adjunctions: Algebras of the induced monad VS. Coalgebras of the induced comonad.

Given an adjunction, we get a monad on one side and a comonad on the other side. What is the connection between their algebra and coalgebra categories? Are they allways equivalent?

The example i have in mind is the starting point of algebraic geometry (or more general: The fundamental theorem of formal concept analysis) ~ the relation between polynomials and points in affine space given by fRx iff f(x)=0 induces an order preserving isomorphism between radical ideals and "algebraic sets".