Editing Heyting algebra (section)

===Category-theoretic definition===
A Heyting algebra <math>H</math> is a bounded lattice that has all [[exponential object]]s.

The lattice <math>H</math> is regarded as a [[category (mathematics)|category]] where 
meet, <math>\wedge</math>, is the [[product (category theory)|product]]. The exponential condition means that for any objects <math>Y</math> and <math>Z</math> in <math>H</math> an exponential <math>Z^Y</math> uniquely exists as an object in <math>H</math>.

A Heyting implication (often written using <math>\Rightarrow</math> or <math>\multimap</math> to avoid confusions such as the use of <math>\to</math> to indicate a [[functor]]) is just an exponential: <math>Y \Rightarrow Z</math> is an alternative notation for <math>Z^Y</math>. From the definition of exponentials we have that implication (<math>\Rightarrow : H \times H \to H</math>) is [[right adjoint]] to meet (<math>\wedge : H \times H \to H</math>). This adjunction can be written as <math>(- \wedge Y) \dashv (Y \Rightarrow -)</math> or more fully as:
<math display="block">(- \wedge Y): H \stackrel {\longrightarrow} {\underset {\longleftarrow}{\top}} H: (Y \Rightarrow -)</math>