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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).
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Birkhoff's HSP theorem in categories other than $\mathbf{Set}$
Fix a category $C$ with finite products and a set $L$ of function symbols (each equipped with an arity in $\mathbb N$).
An $L$-algebra in $C$, $\mathbf A=(A,(f^\mathbf{A})_{f\in L})$, is given by some …