Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent quantitative criteria such as cost, confidence, or implementation choice. In practice, these quantities are often introduced through ad hoc scalarization or by augmenting the resource space, which obscures system structure and increases computational burden. We address this limitation by developing a quantale-enriched theory of co-design. We model resources and functionalities as quantale-enriched categories and design problems as quantale-enriched profunctors, thereby lifting co-design from boolean feasibility to general quantitative evaluation. We show that the fundamental operations of series, parallel, and feedback composition remain valid over arbitrary commutative quantales. We further introduce heterogeneous composition through change-of-base maps between quantales, enabling different subsystems to be evaluated in different local semantics and then composed in a common framework. The resulting theory unifies feasibility-, cost-, confidence-, and implementation-aware co-design within one compositional formalism. Numerical examples on a target-tracking system and a UAV delivery problem demonstrate the framework and highlight how native quantitative enrichment can avoid the architectural and computational drawbacks of boolean-only formulations.

翻译：单调协同设计通过将组件建模为所需资源与提供功能之间的可行性关系，支持组合式工程设计。然而，其标准布尔值形式无法原生表示成本、置信度或实现选择等定量指标。实践中，这些定量指标常通过临时标量化或扩充资源空间引入，这掩盖了系统结构并增加了计算负担。针对这一局限，我们发展了基于量化格的协同设计理论。将资源和功能建模为量化格增强范畴，设计问题建模为量化格增强预层，从而将协同设计从布尔可行性提升至通用定量评估。我们证明，在任意交换量化格上，串联、并联和反馈组合等基本操作仍然保持有效。进一步，通过量化格间基变换映射引入异构组合，使不同子系统可在不同局部语义中评估后统一框架内组合。该理论将可行性、成本、置信度和实现感知的协同设计统一于一个组合式形式体系。通过目标跟踪系统与无人机投递问题的数值示例，展示了该框架如何凭借原生定量增强避免纯布尔公式化的架构与计算缺陷。