<p>This paper establishes a categorical equivalence between the category <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {COL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">COL</mi> </math></EquationSource> </InlineEquation> of complete orthomodular lattices and the category <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathscr {T}\mathbb {ODA}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">T</mi> <mi mathvariant="double-struck">ODA</mi> </mrow> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathscr {T}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">T</mi> </math></EquationSource> </InlineEquation>-based orthomodular dynamic algebras. Complete orthomodular lattices serve as the static algebraic foundation for quantum logic, modeling the testable properties of quantum systems. In contrast, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathscr {T}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">T</mi> </math></EquationSource> </InlineEquation>-based orthomodular dynamic algebras, which are specialized unital involutive quantales, formalize the composition and quantum-logical properties of quantum actions. This result refines prior connections between orthomodular lattices and dynamic algebras, provides a constructive bridge between static and dynamic quantum logic perspectives, and extends naturally to Hilbert lattices and broader quantum-theoretic structures.</p>