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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".
The book expands on the material (approximately 100 pages) [1] in the "Mathematical Preliminaries" [2] section of Knuth's The Art of Computer Programming. Consequently, some readers use it as an introduction to that series of books. Concrete Mathematics has an informal and often humorous style. The authors reject what they see as the dry style ...
Like many categories, the category Man p is a concrete category, meaning its objects are sets with additional structure (i.e. a topology and an equivalence class of atlases of charts defining a C p-differentiable structure) and its morphisms are functions preserving this structure. There is a natural forgetful functor
This makes CGHaus a particularly convenient category of topological spaces that is often used in place of Top. The forgetful functor to Set has both a left and a right adjoint, as described above in the concrete category section. There is a functor to the category of locales Loc sending a topological space to its locale of open sets. This ...
The category of commutative rings, denoted CRing, is the full subcategory of Ring whose objects are all commutative rings. This category is one of the central objects of study in the subject of commutative algebra. Any ring can be made commutative by taking the quotient by the ideal generated by all elements of the form (xy − yx).
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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.
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