A group blog on math, physics and philosophy

- Elementary Observations on 2-Categorical Limits (Apr 18, 2014)
- 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.
- On a Topological Topos (Apr 7, 2014)
- A survey of Peter Johnstone’s “On a Topological Topos”.
- An Exegesis of Yoneda Structures (Mar 24, 2014)
- Motivates the notion of Yoneda structure as an expression of basic notions of category theory in a natural 2-categorical language.
- Review of the Elements of 2-Categories (Mar 9, 2014)
- 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
- Metric Spaces, Generalized Logic, and Closed Categories (Feb 21, 2014)
- Summarizes Lawvere’s “Metric Spaces, Generalized Logic, and Closed Categories” which explores applications of enriched category theory to metric topology.
- Categories of Continuous Functors (Feb 5, 2014)
- Summarizes the orthogonal subcategory problem and its solution, presented in Freyd and Kelly’s “Categories of continuous functors I”
- An Emerging Pattern in Algebra and Topology II (Feb 2, 2014)
- 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.
- An Emerging Pattern in Algebra and Topology I (Feb 1, 2014)
- An emerging pattern in algebra and topology leads to a new notion of representation stability, inspired by homological stability.
- Formal Theory of Monads (Following Street) (Jan 27, 2014)
- Summarizes and contextualizes Street’s 1972 paper “The formal theory of monads.”
- An Elementary Theory of the Category of Sets (Jan 12, 2014)
- Summarizes and contextualizes Lawvere’s 1965 paper “An elementary theory of the category of sets.”
- Kan Extension Seminar applications (Nov 25, 2013)
- 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….
- Announcing the Kan Extension Seminar (Oct 16, 2013)
- Announcement for an online graduate reading course in category theory.
- Mapping (Co)cylinder Factorizations via the Small Object Argument (Sep 16, 2013)
- The enriched version of the algebraic small object argument produces the mapping (co)cylinder factorizations for chain complexes of modules over a commutative ring.
- A Weighted Limits Proof of Monadicity (Jul 10, 2013)
- The proof of Beck’s monadicity theorem is “all in the weights.”

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