Last Update: 2024-04-29. For updates or additions to this page, please send a note to Robin Cockett.


Attendees, Abstracts, and Slides

(1) Geoff Cruttwell (Mount Allison, Canada)
(2) David Spivak (Topos, USA)
(3) C.B. Aberle (Topos and CMU, USA)
(4) Priyaa Srinivasan (Topos, USA)
(5) Dorette Pronk (Dalhousie, Canada)
(6) Kristine Bauer (Calgary, Canada)
(7) Jean-Simon Lemay (Macquarie, Australia)

    Title: Drazin Inverses in Categories
    Abstract: Drazin inverses are a special kind of generalized inveres that have been extensively studied with many applications in ring theory, semigroup theory, and matrix theory. Drazin inverses can also be defined for endomorphisms in any category.  In this tutorial, I will give an introduction to Drazin inverses from a categorical perspective. The talk is based on the paper which is joint work with Robin Cockett and Priyaa Srinivasan.


(8) Rick Blute (Ottawa, Canada)
(9) Robin Cockett (Calgary, Canada)
(10) Amolak Ratan (Waterloo, Canada)
(11) Marcello Lanfranchi (Dalhousie, Canada)
(12) Florian Schwarz (Calgary, Canada)
(13) Susan Niefield (Union College, USA)

    Title: Adjoints in double categories
    Abstract: We present three double categories of quantales.  The first  is strict, the second is pseudo, and the third is actiualy a double bicategory.  Along the way we encounter quantale-values relations, projective modules, companions, conjoins, adjoint bimodules, and Cauchy completeness.  The strict bicategory is Cauchy (i.e. every object is Cauchy complete). The pseudo one is not, but this is corrected using the Kleisli bicategory of a graded monad as part of the double bicategory.

(14) Laura Scull (Fort Lewis College, USA)
(15) Samuel Desrochers (Ottawa, Canada)
(16) Rory Lucyshyn-Wright (Brandon, Canada)
(17) Alexanna Little (Calgary, Canada)
(18) Melika Norouzbegi (Calgary, Canada)
(19) Saina Daneshmandjar (Calgary, Canada)
(20) Durgesh Kumar (Calgary, Canada)
(21) Adrian Tadic (Calgary, Canada)
(22) Elahe Lotfi (Calgary, Canada)
(23) Katrina Honigs (Simon Fraser, Canada)
(24) Shayesteh Naeimabadi (Ottawa, Canada)
(25) Martin Frankland (Regina, Canada)
(26) Jonathan Funk (CUNY, USA)

    Title: Toposes and C*-algebras
    Abstract: We define and study a certain left cancellative category and topos associated with a C*-algebra. The topos we define is inspired by and to some extent resembles what is done in pseudogroup and inverse category theory, while recognizing that for a C*-algebras there are distict and novel points of departure from the semigroup constructions.  We work under the hypotjhesis we call a supported C*-algebra, which means that the algebra has enough projections in a certain sense. We shall establish a topos interpretation of the so called polar decomposition of an operator. Thiis intepretation is part of a correspondence between quotients of a torsion-free generator of the topos af the C*-algebra, and certain subcategories of the left-cancellative category of the algebra.

(27) Cole Comfort (Univ. Loraine, France)
(28) Aaron Fairbanks (Dalhousie, Canada)
(29) Samuel Steakley (Calgary, Canada)
(30) Jean Baptiste Vienney (Ottawa, Canada)

    Title: A sequent calculus for commutative distributive lattice ordered monoids
    Abstract: In what logic does elementary arithmetic happen? Many aspects of divisibility are captured by the notion of commutative distributive lattice-ordered monoid. I will present a sequent calculus for this structure. The decidability of the equational theory of commutative distributive lattice-ordered monoids is presented as open in the recent literature. If this sequent calculus has cut elimination then it implies this decidability. A main point of the talk will thus be whether the sequent calculus has cut elimination or not.

(31) Matthew Di Meglio (Edinburgh, UK)
(32) Geoff Vooys (Dalhousie, Canada)
(33) Robert Morissette (Dalhousie, Canada)
(34) Rose Kudzman-Blais (Ottowa, Canada)
(35) David Sprunger (Indiana State,USA)
(36) Amelie Comtois (Ottawa, Canada)
(37) Sam Winnick (Waterloo, Canada)
(38) Sacha Ikonicoff (Strasbourg, France)
(39) César Bardomiano (Ottawa, Canada)

    Title: The language of a model category
    Abstract: Quillen model categories are a cornerstone for modern homotopy theory. These categories, originally devised to capture homotopical properties of categories like topological spaces, simplicial sets or chain complexes, have gained relevance for giving a way to construe higher categories which are of great importance, for example, in algebraic topology and geometry. In this talk, we will see that model categories also have logical information on their own in the following sense: Given any model category, we can associate to it a class of first-order formulas referring to the fibrant objects of the category. For example, the associated language of the category of small categories, equipped with its canonical model structure, coincides with language for categories defined by Blanc [1] and Freyd [2], whose central feature is that it respects the equivalence principle. Similarly, the language we associate to a model category respects the appropriate version of the equivalence principle: two homotopically equivalent objects satisfy the same formulas and replacing parameters by homotopically equivalent ones does not change the validity of a formula. Finally, we will show that for M and N two Quillen equivalent model categories, their associated languages are, suitably, equivalent.

(40) Rachel Hardeman Morill (Calgary, Canada)

Last Update: 2024-04-29. For updates or additions to this page, please send a note to Robin Cockett.

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