[Alta-Logic] Peripatetic seminar

[Matthew Burke]

Speaker: Daniel Satanove

Date and time: Tuesday, January 29th, 2019 at 12:15

Location: MS 337

Title: Presentations of Theories

Abstract: Every algebraic theory T with set of sorts S has a notion of free functor from the category Set^S which is constructed uniformly by Kan extension of models along the canonical interpretation, a functor between classifying categories, Cl(S) -> Cl(T) (where S is considered as a theory with no operations). This can be seen as a uniform way of constructing syntax for algebraic theories - the free functor sends a set of generators to the set of words formed by the operations of the theory on those generators. Furthermore, every object M in the categories of models Mod(T) is isomorphic to a presentation by free objects. In the case of groups, this is the familiar notion of a presentation by generators and relations < X | R >. Parts of this picture extend to essentially algebraic theories via sketches and Gabriel-Ulmer duality. I look at ways of getting a more complete picture and apply it to classifying categories for algebraic and essentially algebraic theories, so that the process of generating classifying categories can be seen as the same sort of syntax generation as for free groups and free algebras of algebraic theories.

http://peripatetic-seminar.cpsc.ucalgary.ca/wp/