symmetric monoidal (∞,1)-category of spectra Let and be algebraic theories. The category of -bimodels and their homomorphisms is the category of -models and homomorphisms in . An alternative description is that it is a co--model in . Each such bimodel determines and is determined by a pair of adjoint functors Composition of such adjoint pairs yields a functor The category has a unit object – it would be churlish not to overload our notation yet further by calling it , corresponding to the fact..