1. Rickard or derived equivalences as a generalization of Morita equivalences of rings and algebras are named after him.

2. It follows that adjoint functors induce homotopy equivalences.

3. Equivalences of gas accumulation infer a pre-eruption crystallization.

4. If theoretical training is by correspondence, equivalences with the above‐mentioned lessons shall be determined.

5. If and are inverse functors, the corresponding monad is the identity functor.In general, Adjunctions are not equivalences—they relate categories of different natures

6. The algebraic notion of congruence can also be generalized to partial equivalences, yielding the notion of subcongruence, i.e. a homomorphic relation that is symmetric and transitive, but not necessarily reflexive.