A subresiduated lattice is a pair (A, D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every \(a,b\in A\) there is \(c\in D\) such that for all \(d\in D\), \(d\wedge a\le b\) if and only if \(d\le c\). This c is denoted by \(a\rightarrow b\). This pair can be regarded as an algebra \(\left<A,\wedge ,\vee ,\rightarrow ,0,1\right>\) of type (2, 2, 2, 0, 0) where \(D=\{a\in A\mid 1\rightarrow a=a\}\). The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices.

子残差格是一对 ( A ,  D )，其中A是有界分布格，D是A的有界子格，对于每个\(a,b\in A\)有\(c\in D\)这样对于所有\(d\in D\)，\(d\wedge a\le b\)当且仅当\(d\le c\)。这个c由\(a\rightarrow b\) 表示。这对可以看作是(2, 2, 2, 0, 0) 类型的代数\(\left<A,\wedge ,\vee ,\rightarrow ,0,1\right>\ ) 其中\(D= \{a\in A\mid 1\rightarrow a=a\}\). 子残差格的类是适当包含各种 Heyting 代数的变体。在本文中，我们提出了子残差格的代数范畴的对偶等价。更准确地说，我们为这个代数范畴开发了一个谱式对偶性和一个位拓扑式对偶性。最后，我们研究了这些结果与子残差格的代数范畴的已知 Priestley 式对偶性的联系。