Definition
Specified base field F
Specified base field F with its specified scalar field, operations, and categorical structure.
A specified base field is a field carried as an explicit parameter of a categorical comparison. Its addition, multiplication, zero and unit are fixed; the symbol does not denote a universal field containing all the other catalogue fields.
Keeping the parameter fixed
An -linear map must commute with this specified scalar action. An -algebra map must also preserve multiplication, and in a unital algebra category preserve the unit. Changing the parameter changes the category, so diagrams from different choices cannot be composed merely because their labels both say .