Implicit Structure of Concrete Categories
Given a concrete category (C,U) and a cardinal number N, let UN be the functor C → Set determined by UN(c) = (U(c))N. Then a subfunctor of UN is called an N-ary predicate and a natural transformation UN → U an N-ary operation.
The class of all N-ary predicates and N-ary operations of a concrete category (C,U), with N ranging over the class of all cardinal numbers, forms a large signature. The category of models for this signature then contains a full subcategory which is equivalent to C.
Read more about this topic: Concrete Category
Famous quotes containing the words implicit, structure, concrete and/or categories:
“A piece of advice always contains an implicit threat, just as a threat always contains an implicit piece of advice.”
—José Bergamín (1895–1983)
“Slumism is the pent-up anger of people living on the outside of affluence. Slumism is decay of structure and deterioration of the human spirit. Slumism is a virus which spreads through the body politic. As other “isms,” it breeds disorder and demagoguery and hate.”
—Hubert H. Humphrey (1911–1978)
“Don’t feel guilty if you don’t immediately love your stepchildren as you do your own, or as much as you think you should. Everyone needs time to adjust to the new family, adults included. There is no such thing as an “instant parent.”
Actually, no concrete object lies outside of the poetic sphere as long as the poet knows how to use the object properly.”
—Johann Wolfgang Von Goethe (1749–1832)
“Kitsch ... is one of the major categories of the modern object. Knick-knacks, rustic odds-and-ends, souvenirs, lampshades, and African masks: the kitsch-object is collectively this whole plethora of “trashy,” sham or faked objects, this whole museum of junk which proliferates everywhere.... Kitsch is the equivalent to the “cliché” in discourse.”
—Jean Baudrillard (b. 1929)