194 citations · 1.2k across the 78 of their papers we have counts for
9 papers · 1 filter
On the Pre- and Promonoidal Structure of Spacetime
James Hefford, Aleks Kissinger
The notion of a joint system, as captured by the monoidal (a.k.a. tensor) product, is fundamental to the compositional, process-theoretic approach to physical theories. Promonoidal…
Rewriting modulo symmetric monoidal structure
Filippo Bonchi, Fabio Gadducci, Aleks Kissinger +2
String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming in…
A first-order logic for string diagrams
Aleks Kissinger, David Quick
Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of inf…
Finite matrices are complete for (dagger-)hypergraph categories
Aleks Kissinger
Hypergraph categories are symmetric monoidal categories where each object is equipped with a special commutative Frobenius algebra (SCFA). Dagger-hypergraph categories are the same…
Abstract Tensor Systems as Monoidal Categories
Aleks Kissinger
The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To…
Completely positive projections and biproducts
Chris Heunen, Aleks Kissinger, Peter Selinger
The recently introduced CP*-construction unites quantum channels and classical systems, subsuming the earlier CPM-construction in categorical quantum mechanics. We compare this con…