nLab amalgamation

Traditionally:

• in group theory

  1. the term amalgamated free product of groups refers to what really are pushouts in the category Grp, while

  2. the plain term “free product” really refers to coproducts in the category Grpd;

therefore it makes sense to generally agree that:

• in category theory the term “amalgamated sum” [Gabriel & Zisman (1967), p. 1] and variants like “amalgamated coproduct” or just “amalgamation” refers to pushouts (seen, if you will, as coproducts in a coslice category).

Beware though, while the terminology “amalgamation” indeed neatly captures the nature of pushouts in general categories, traditionally it is not widely used in this generality.

Moreover, but only vaguely related:

• in model theory there is a notion of amalgamation property of structures in model theory.

Finally, the term amalgamation theory is used here and there…

category: disambiguation