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)
(41) Jack Jia (Dalhousie, Canada)
Last Update: 2024-04-29. For updates or additions to this
page, please send a note to Robin
Cockett.
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