The aim is to use string diagrams to represent simply-typed lambda calculus terms so that computation may be modeled by the idea of a sequence of rewriting steps of string diagrams, providing an operational semantics.
We discuss some of the limitations that the measure-theoretic probability framework has in handling uncertainty and present some other formal approaches to modelling it, an introduction to the study of imprecise probabilities from a mathematical perspective.
In the Part 1 of this post, we saw how logical equivalences of first-order logic (FOL) can be characterised by a combinatory game. But there are still a few unsatisfactory aspects, which we’ll clear up now.
LDCs are categories with two tensor products linked by coherent linear (or weak) distributors. The significance of this theoretical development stems from many situations in logic, theoretical computer science, and category theory where tensor products play a key role.
A central idempotent in a monoidal category $(\mathbf{C}, \otimes, I)$ is a way to speak about the “location” of a process taking place in $\mathbf{C}$, but without referring to points, space, or distance.
Let’s motivate this blog post by first formalizing what a resource theory is. Coecke et al. represent a resource theory in “A mathematical theory of resources” as a symmetric monoidal category (SMC), which is a familiar construction in applied category theory.
Job announcement for a postdoctoral position in higher category theory, homotopy type theory, especially as related to quantum logic or quantum field theory at Johns Hopkins.
Guest post by Chris Kapulkin Two years ago, I wrote a post for the n-Cafe, in which I sketched how to make precise the claim that intensional type theory (and ultimately HoTT) is the internal language of higher category…
This post explains the meaning of “the comprehension construction,” the title of a recent paper by Riehl and Verity (https://arxiv.org/abs/1706.10023).
An expository summary of Hyland and Power’s “The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads” for the Kan Extension Seminar II.
A little bird tells me that Macquarie University is hiring (even more) category theorists! Specifically, they are offering two-year research fellowship positions, details of which can be found here. Macquarie University, which is in greater Sydney, is the home…
Summarizes the approach to coherence theorems expressed as a rectification for pseudoalgebras for a 2-monad using codescent objects, following Steve Lack.
Summarizes “A Classification of Accessible Categories,” which characterizes those categories that are locally presentable or accessible relative to a sound limit doctrine.
Describes Kelly’s “Elementary observations on 2-categorical limits” and the general theory of weighted limits and colimits, which are described here in a special case.
Summarizes the paper of Kelly and Street “Review of the elements of 2-categories” containing common background material for papers in the Sydney Category Seminar Lecture Notes 420
Summarizes Lawvere’s “Metric Spaces, Generalized Logic, and Closed Categories” which explores applications of enriched category theory to metric topology.
An emerging pattern in algebra and topology leads to a new notion of finitely generated FI-modules, which capture the representation stable sequences that arise in practice.
A friendly reminder: applications for the Kan Extension Seminar are due at the end of the week. More information can be found in the initial announcement and on the seminar website. For those who don’t enroll, watch this space….
The enriched version of the algebraic small object argument produces the mapping (co)cylinder factorizations for chain complexes of modules over a commutative ring.