**Warning: Incomplete!**

July 4, 2000

Bob Paré

*Free double categories and the word problem for groups, II*

July 11, 2000 Margaret Beattie

*Quasi isomorphism of finite dimensional Hopf algebras*

**Abstract**: Roughly the idea is this: There are now lots of counter examples to Kaplansky's Tenth Conjecture, which states that for a given finite dimension n , there are only finitely many Hopf algebras of dimension n up to isomorphism. However, all the known families of non-isomorphic Hopf algebras of a given dimension contain only finitely many quasi- isomorphism classes. Two Hopf algebras are called quasi-isomorphic if their categories of comodules are monoidally equivalent. About half the seminar will be a discussion of quasi-isomorphism (Ulbrich, Schauenburg), then Masuoka's theorem and an example.

September 5, 2000

Claudia Centazzo

*An Extension of the Regular Completion*

**Abstract**: Carboni's regular completion of a lex category provides a KZ-doctrine on

**lex}**, the algebras for which are regular categories. Our idea is to describe a KZ-doctrine on

**cat**which `lifts' to

**lex**to give Carboni's doctrine. Such a result would exhibit

**reg**as the algebras for a distributive law of the coKZ monad, whose algebras are lex categories, over the required KZ-doctrine on

**cat**. We achieve a KZ-doctrine on the 2-category

**cat**_kerarr of all categories, kernel arrow-preserving functors and all natural transformations, which does, when restricted, to

**lex**give Carboni's doctrine. The algebras for our doctrine are the categories with a regular factorization system (in the sense of Kelly).

September 12, 2000

Bob Paré

*Free Double Categories and the Word Problem for Groups*

RJ Wood

*Why op-monadic functors compose*

**Abstract:**(The second talk will be in the spirit of what I suggested a few weeks ago for alternative talks --- rather pedagogical, not particularly new but of wide interest and applicability. Last year Bob Pare gave a series of talks on monadicity in this vein. They were very successful and I will try to continue the theme. Probably it will take two instalments to complete.)

September 19, 2000

RJ Wood

*Why op-monadic functors compose II*

**Abstract:**I will attempt to wrap up with this talk. I will prove the `FTT', note the dual theorem and apply both in the bicategory of profunctors. `Bijective on objects' will get a conceptual definition that makes sense in more general bicategories. Time permitting we will show how interpretation of the results in bicategories of toposes exhibits the `surjection-inclusion' factorization of geometric morphisms as a special case.

September 26, 2000

Dale Garraway

*Presheaves and sheaves for a quantaloid*

October 3, 2000

Dorette Pronk

*Orbifold Cohomology*

**Abstract:**The orbifold cohomology and homotopy groups are invariants which are used in various parts of mathematics and other sciences such as physics and crystallography. In this talk I will introduce orbifolds and several ways of representing them, which can be used to either define or calculate these groups. I will also discuss the use of orbifolds in quantum field theory.