Department of Mathematics

The Graduate Center of The City University of New York

365 Fifth Avenue (at 34th Street) map

(Diagonally across from the Empire State Building)

New York, NY 10016-4309

Wednesdays 7:00 - 8:30 PM.

Room 6417 .

Contact N. Yanofsky to schedule a speaker

or to add a name to the seminar mailing list.

The New York Category Theory Seminar and the New York Haskell Meetup is sponsoring a

The book is about the field of Topos Theory, which is a vast generalization of a number of fields, giving a categorical intersection between type theory, logic, and also geometry. No prior knowledge of category theory will be required, although the introductory sections on the basics are a bit whirlwind, so at least mild familiarity with the definition of a category, a functor, and a natural transformation will certainly help. If you have been interested in learning more about categories, this will be a good place to start to see them in action towards interesting ends. The list for announcements and scheduling regarding this group is also at the hott-nyc google group:

https://groups.google.com/forum/#!forum/hott-nyc

While prior, people may have understood that acronym to mean "homotopy type theory" (which was our prior group read project, now completed), with a slight change in perspective the acronym can be read to refer to "Homotopy or Topos Theory" :-). As with that group read, we plan to meet the first and third wednesday of every month, working as slowly as necessary through bite-sized pieces.

Also, as with the prior group read, this is meant to be a place where people with mild background in any number of different fields can interact, and which is welcoming to people with only modest knowledge to begin with. The aim is to read and learn together, each bringing our own intuitions, backgrounds, and experiences to the table.

We meet the first and third Wednesdays of each month from 7:00 to 8:30 PM in Room 6417. The meetings are run by Gershom Bazerman and Dustin Mulcahey.

This talk will survey some of what has been done, centered on constructions of final coalgebras for various functors.

For background, I suggest http://plato.stanford.edu/entries/nonwellfounded-set-theory/ especially Section 4.

THEOREM: A topos EE has a globally supported isotropically free object iff it has a globally supported isotropically trivial object O such that EE/O is equivalent to B(FF;G), where G is group internal to an anisotropic topos FF.

The interpretation of the theorem for inverse semigroups reveals some basic, but nevertheless illuminating facts about inverse semigroups and their relationship with toposes.

Joint work with Pieter Hofstra (University of Ottawa) and Ben Steinberg (City College, CUNY)

We show how to mathematically model the two versions starting just with a subset S of U and then focus on the less familiar #2 interpretation where S is viewed not as a set of distinct elements but as a more abstract entity 'S-ness' that is definite on what is common between the elements of S and indefinite on how they differ. The point is that the #2 case dovetails precisely with the quantum mechanics notion of a superposition of distinct eigenstates of some observable which is a state definite only on what is common to the superposed eigenstates and is objectively or onticly indefinite between them. The process in general of classifying by some attribute to make the #2 indefinite state more definite then emerges as the process of measurement in QM.

Previous Semesters:

##### Fall 2013 - Spring 2015 Homotopy Type Theory Reading Group

##### Spring 2012

##### Fall 2011

##### Spring 2011

##### Fall 2010

##### Spring 2010

##### Fall 2009

##### Spring 2009

Other Category Theory Seminars: