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:
“To revolt is a natural tendency of life. Even a worm turns against the foot that crushes it. In general, the vitality and relative dignity of an animal can be measured by the intensity of its instinct to revolt.”
—Mikhail Bakunin (1814–1876)