University of Calgary

Cartesian Differential Categories are defined to introduce and study the notion of differential from calculus in a category theory point of view. In a Cartesian Differential Category, morphisms between objects can be « derived », and this...

It is known that the category of affine Lagrangian relations over a field F, of integers modulo a prime p (with p > 2) is isomorphic to the category of stabilizer quantum circuits for p-dits. Furthermore, it is known that electrical circuits...

Richard Guy loved problems. He loved to share them and to encourage others to explore them. He loved to work with superstars like John Conway and make their ideas accessible to a wider world. But Richard also had a few problems that he obsessed on in...

Mathematics has developed an increasingly “higher dimensional” point of view of when different things deserve the same name, categorifying the traditional logical notion of equality to isomorphism (from Greek isos “equal” and morphe “form” or “shape”...

A partial monoid is a set A with a multiplication and a unit, but the multiplication is only defined on a certain subset of pairs. This means the multiplication m:AxA -> A is a partial map, a map that is only defined on a certain subset of its domain...

This is a report from team Functor Calculus at the 4th Women in Topology conference. In earlier work, K. Hess and B. Johnson invented a way of producing what they call “calculus towers” from comonads. These calculus towers generalize functor calculus...

In 1973, C. I. Lewis published a landmark text developing a theory of counterfactual logics. The primary goal of the text was in providing a logical framework where one could reason about sentences of the form: “if P were true, then Q would be true”...

Vector bundles and principal bundles are important objects in differential geometry. Vector bundles over a manifold M are manifolds that are locally isomorphic to the Cartesian product M times V for some vector space V, while principal bundles over M...

Quillen-Barr-Beck (co)homology is a theory which studies the objects of a category where we can make sense of such notions as “modules” and “derivations”. More precisely, in his thesis, Beck defined a general notion of modules and derivations in a...