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A concrete category is a pair (C,U) such that . C is a category, and; U : C → Set (the category of sets and functions) is a faithful functor.; The functor U is to be thought of as a forgetful functor, which assigns to every object of C its "underlying set", and to every morphism in C its "underlying function".
This forms a category because the composition of two C p maps is again continuous and of class C p. One is often interested only in C p-manifolds modeled on spaces in a fixed category A, and the category of such manifolds is denoted Man p (A). Similarly, the category of C p-manifolds modeled on a fixed space E is denoted Man p (E).
This is a list of building materials.. Many types of building materials are used in the construction industry to create buildings and structures.These categories of materials and products are used by architects and construction project managers to specify the materials and methods used for building projects.
The following definition translates this to any category. A concrete category is a category that is equipped with a faithful functor to Set, the category of sets. Let C be a concrete category with a faithful functor U : C → Set. Let X be a set (that is, an object in Set), which will be the basis of the free object to be defined.
Right now, Lalgee said, many companies are struggling to gain loyalty from employees. In the recruitment universe, he said, he hears comments all the time about how many younger people don’t ...
Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about abelian categories; it essentially states that these categories, while rather abstractly defined, are in fact concrete categories of modules. This allows one to use element-wise diagram chasing proofs in
A 17-year-old cheerleader from California was stabbed to death just days before Christmas — and police say they've arrested an "acquaintance" in connection with the case. On Friday, Dec. 20, at ...
Traveling on Turkey Day? Make sure to carve out some extra time. This Thanksgiving is expected to be the busiest ever for air travel, with a record-setting 18 million Americans expected to jet off ...