A database of mathematical structures and classes, based on concrete categories. Classes of structures are defined axiomatically, by a list of axioms that define the structures in the class, and the morphisms between them. \(\)\(\bb N\)For example, the class of posets, with \(p\)-morphisms is defined as the class of structures \(\left(P,\le\right)\) such that \(x\le x\)\(x\le y\ \text{and}\ y\le x\ \Rightarrow\ x=y\)\(x\le y\ and\ y\le z\Rightarrow x\le z\)and for posets \(\left(P,\le\right),\left(Q,\le\right)\) a p-morphism from \(P\) to \(Q\) is a function \(f:P\to Q\) such that \(x\le y\Rightarrow f\left(x\right)\le f\left(y\right)\) and f(u) <= v’ implies there exists v ∈ W such that u <= v and f(v) = v’.