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is just an exponential: is an alternative notation for . From the definition of exponentials we have that implication ($\{\backslash Rightarrow:\; H\; \backslash times\; H\; \backslash to\; H$)}} is right adjoint to meet ($\backslash wedge\; :\; H\; \backslash times\; H\; \backslash to\; H$). This adjunction can be written as or more fully as:

Lattice-theoretic definitions

An equivalent definition of Heyting algebras can be given by considering the mappings:

for some fixed a in H. A bounded lattice H is a Heyting algebra if and only if

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