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.