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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".
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.
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.
These categories are characterized by the fact that every structured source has a unique initial lift (). In Top the initial lift is obtained by placing the initial topology on the source. Topological categories have many properties in common with Top (such as fiber-completeness, discrete and indiscrete functors, and unique lifting of limits).
The latest officially released version of MasterFormat is the 2018 Edition, which uses the following Divisions: PROCUREMENT AND CONTRACTING REQUIREMENTS GROUP:
Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas ...
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Stamped concrete is an architectural concrete that has a superior surface finish. After a concrete floor has been laid, floor hardeners (can be pigmented) are impregnated on the surface and a mold that may be textured to replicate a stone / brick or even wood is stamped on to give an attractive textured surface finish.