A Cook's Tour of Other Universal Constructions

By Bergman, G. M.

Book Id: WPLBN0000667874
Format Type: PDF eBook
File Size: 301.04 KB
Reproduction Date: 2005

Title:	A Cook's Tour of Other Universal Constructions
Author:	Bergman, G. M.
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Bergman, G. (n.d.). A Cook's Tour of Other Universal Constructions. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: We shall now look at a number of other constructions having many similarities to that of free groups. In each case, the construction can be motivated by a question of the form, ??Suppose we have a structure about which we know only that it satisfies such and such conditions. How much can we say about it on the basis of this information alone??? In favorable cases, we shall find that if we collect the ??data?? we can deduce about such an object, this data itself can be made into an object F, which satisfies the given conditions, and satisfies no relations not implied by these (cf. remark 2.2.10). This F is then a ??universal?? example of these conditions, and that fact can be translated into a ??universal mapping property?? for F...