Adjoints and Monads Related to Compact Lattices and Compact Lawson Idempotent Semimodules

摘要

For compact Hausdorff Lawson lattices L that are idempotent semirings with lower semicontinuous multiplications, free compact Hausdorff Lawson L-idempotent semimodules are constructed over compacta and over compact Hausdorff Lawson lower semilattices. It is shown that these free objects are spaces of L-valued regular measures. Related left adjoint functors and monads are described.