Search results
Results from the WOW.Com Content Network
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 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.
Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way. Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B.
Download QR code; Print/export Download as PDF; ... Pages in category "Concrete" The following 200 pages are in this category, out of approximately 221 total.
These categories of materials and products are used by architects and construction project managers to specify the materials and methods used for building projects. Some building materials like cold rolled steel framing are considered modern methods of construction , [ by whom? ] [ clarification needed ] over the traditionally slower methods ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The zero objects in Grp are the trivial groups (consisting of just an identity element). Every morphism f : G → H in Grp has a category-theoretic kernel (given by the ordinary kernel of algebra ker f = {x in G | f(x) = e}), and also a category-theoretic cokernel (given by the factor group of H by the normal closure of f(G) in H).
Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.