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Power topological molecular lattice category and its product operation. (Chinese. English summary) Zbl 1047.18007

Summary: Four categories, power molecular lattice category, \(L\)-base power molecular lattice category, power topological molecular lattice category and \(L\)-base power topological molecular lattice category, are defined. The relations between power molecular lattice and molecular lattice categories, \(L\)-base power molecular lattice and power molecular lattice categories, power topological molecular lattice and topological molecular lattice categories, and \(L\)-base power topological molecular lattice and power topological molecular lattice categories are discussed. It is proved that a \(\otimes\)-product of power molecular lattices is the product in power molecular lattice category, a product of \(L\)-base power molecular lattices is the product in \(L\)-base power molecular lattice category, a \(\otimes\)-product of power topological molecular lattices is the product in power topological molecular lattice category, and a product of \(L\)-base power topological molecular lattices is the product in \(L\)-base power topological molecular lattice category.

MSC:

18B35 Preorders, orders, domains and lattices (viewed as categories)
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
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