Is it naive to ask that universal algebra theory should also include partial algebras, and in particular groupoids, categories, multiple groupoids, multiple categories (of various kinds)?
It seems that where the methods of universal algebra generalize well to cover partial algebras is in _essentially_ algebraic theories, i.e. those in which there is a hierarchy of operators such that the domain of definition of each is defined by a conjunction of equations involving more primitive operators. This certainly covers categories and groupoids - anyone who knows Phillip Higgins' book can see how smoothly universal algebra works for them. As for multiple groupoids and multiple categories, I can't say because I'm not familiar with them. As far as the partial case is concerned: why not generalized algebraic theories ala Cartmell? They seem to have essentially the same basic semantic interpretation (categories with finite limits) and are applicable to similar examples. I prefer generalized algebraic theories because they are essentially a first order subset of Type Theory (ala Martin L"of) which is used by many people in Computer Science to formalize mathematics and to verify algorithms. I personally also find generalized algebra more natural, e.g. when formalizing catgeories (why not call them monoidoids ?) one introduces homsets and composition as indexed by the objects instead of having cod and dom and composition as a partial operation. Thorsten Altenkirch Host: muppet77.cs.chalmers.se Office: 2438 snail: Dep. of Computer Sciences; Chalmers U. of Technology; 412 96 Gothenburg phone: (+ 46) 31 772 1079 [office], (+ 46) 31 55 54 40 [home] Sweden ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++