Le vendredi 25 Novembre 2005 04:56, duraid@octopus.com.au a écrit :
Is there an accepted terminology for semigroups with many objects, i.e. gadgets that satisfy the all the axioms satisfied by categories excepting those which refer to identities ?
Koslowski calls these "taxonomies", see e.g. "Monads and interpolads in bicategories" (TAC vol 3, no 8 (1997)).
Duraid
Dear all, I call a "small semigroup with many objects enriched over the model category of compactly generated topological spaces" a "flow" in my work (these objects are interesting for me only if they are enriched over very particular model categories satisfying particular properties). The terminology comes from the fact that I use them to study the time flow of a higher dimensional automaton (up to directed homotopy). For "taxonomy", I would be very curious to know the origin of the terminology. What does it mean exactly ? In the paper q-alg/9608025 "Flexible sheaves", Carlos Simpson calls a "(not necessarily small) semigroup with many objects enriched over the category of topological spaces" a continuous semicategory. I had also seen the word "precategory" but I cannot remember where. Beware of the fact that the word precategory is also used for categories *with identities* such that the composition law is partially defined : that is the fact that the codomain of F is equal to the domain of G is not sufficient for GoF to exist. Once again, I cannot remember where I read this word. The only thing I remember is that that was a computer-scientific work. The word "non-unital category" is also used sometime in mathematical papers. pg.