We develop the theory of weak Fraïssé categories, in which the crucial concept is the weak amalgamation property, discovered relatively recently in model theory. We show that, in a suitable framework, every weak Fraïssé category has its unique generic limit, a special object in a bigger category, characterized by a certain variant of injectivity. This significantly extends the present theory of Fraïssé limits.
Keywords: Weak amalgamation property, generic object, Fraïssé limit
2020 MSC: Primary 03C95; Secondary 18A30
Theory and Applications of Categories, Vol. 38, 2022, No. 2, pp 27-63.