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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 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.
Pages in category "Concrete" The following 200 pages are in this category, out of approximately 221 total. This list may not reflect recent changes.
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).
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.
We'll cover exactly how to play Strands, hints for today's spangram and all of the answers for Strands #317 on Tuesday, January 14. Related: 16 Games Like Wordle To Give You Your Word Game Fix ...
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.
Freddie Mac reports an average 6.91% for a 30-year fixed-rate mortgage, up 6 basis points from last week's average 6.85%, according to its weekly Prime Mortgage Market Survey of nationwide lenders ...