We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces relative to weak generalized controlled deformation retracts. On ordinary coarse cohomology, our secondary cup product agrees with a secondary product defined by Roe. For coarsifications of topological coarse (co-)homology theories, our secondary cup and cap products correspond to the primary cup and cap products on Higson dominated coronas via transgression maps. And in the case of coarse \(\mathrm {K}\)-theory and -homology, the secondary products correspond to canonical primary products between the \(\mathrm {K}\)-theories of the stable Higson corona and the Roe algebra under assembly and co-assembly.

我们根据给定的交叉和倾斜乘积的粗（共）同调理论构造二级杯和帽乘积。它们是为相对于弱广义受控变形缩回的粗糙空间而定义的。在普通粗上同调上，我们的二次杯乘积与 Roe 定义的二次乘积一致。对于拓扑粗（共）同调理论的粗化，我们的次级杯和帽产品通过海侵图对应于 Higson 主导的日冕上的初级杯和帽产品。在粗糙的\(\mathrm {K}\) -理论和 -同源性的情况下，二次产品对应于稳定 Higson 电晕和 Roe的\(\mathrm {K}\) -理论之间的规范一次产品代数装配和协同装配。