Relative Concreteness
In some parts of category theory, most notably topos theory, it is common to replace the category Set with a different category X, often called a base category. For this reason, it makes sense to call a pair (C,U) where C is a category and U a faithful functor C → X a concrete category over X. For example, it may be useful to think of the models of a theory with N sorts as forming a concrete category over SetN.
In this context, a concrete category over Set is sometimes called a construct.
Read more about this topic: Concrete Category
Famous quotes containing the word relative:
“Man may have his opinion as to the relative importance of feeding his body and nourishing his soul, but he is allowed by Nature to have no opinion whatever as to the need for feeding the body before the soul can think of anything but the body’s hunger.”
—George Bernard Shaw (1856–1950)