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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".
Kernels are familiar in many categories from abstract algebra, such as the category of groups or the category of (left) modules over a fixed ring (including vector spaces over a fixed field). To be explicit, if f : X → Y is a homomorphism in one of these categories, and K is its kernel in the usual algebraic sense , then K is a subalgebra of ...
The 16 Divisions of construction, as defined by the Construction Specifications Institute (CSI)'s MasterFormat, is the most widely used standard for organizing specifications and other written information for commercial and institutional building projects in the U.S. and Canada.
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.
Texas is looking at a plan to ramp up migrant buses again — but instead of sending them to sanctuary cities, officials would ship newly arrived illegal migrants directly to ICE holding centers ...
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 ...
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 ...
A Canadian woman allegedly attempted to smuggle 22 pounds of methamphetamine wrapped as Christmas presents through a New Zealand airport on Sunday, Dec. 8.