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The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).
3
votes
Universal constructions that factor through endomorphisms
From Hodges, model theory, section 9.3 Word-constructions pag. 431:
There is no agreed name for functors $\Gamma$ as defined above. To category theorists they are the left adjoints of forgetful funct …
2
votes
Accepted
Axiomatizing orientation in the complex plane
A too long waste of bits in three parts. The core of the answer is the summary at the end of part 2 section 2.
Part 1. Orientation.
Before treating the aspects on which I agree, let me say one aspec …
2
votes
IBN for algebraic theories
A. Has the IBN property for algebraic theories in general been studied in the literature?
Yes, mostly by many polish authors. See Gr\"atzer, universal algebra, Chap. 5.
For example, at pag. 198 …