Changes

Below you find an overview of the updates to the Clowder project.

2025

July 06

• •The right adjoint $f_{*}$ to the inverse image functor for powersets $f^{-1}\colon\mathcal{P}(Y)\to\mathcal{P}(X)$ is now called the codirect image.
• •Notation for the left/right adjoints to inverse images of powersets has been changed; see Tag 0225.
• •Fixed an issue with duplication of tags, in which some tags unfortunately had to be changed as a result. (Although this goes against the principle of tags, I've decided to go forward with it at this specific moment in time because Clowder doesn't really currently seem to be used that much anyway.)
• •Added an introduction to the project, Tag 01WK.
• •Made Clowder's compilation process reproducible via GitHub Actions.
• •Completely reworked Clowder's infrastructure, fixing several bugs and implementing a number of quality-of-life features. This took months; there are simply too many changes to individually list here! See here for a description of some of the most notable new features.

2024

December 04

• •Revised and added new material on moduli of monoidal structures to Constructions With Monoidal Categories.
• •Revised Tag 01QW.
• •Added a completely 1-categorical proof of the universal property of the smash product of pointed sets, Tag 01VY, answering MO 466593.

November 22

• •Added some missing proofs to Chapter: Pointed Sets.

November 19

• •Began a complete overhaul of all proofs which read “Clear.” and the like. All proofs must now read either “Omitted” or be properly justified, no matter how “trivial” the details are.
• •Footnote sections are now local with respect to each environment box.
• •Heavily modified Chapter: Constructions With Sets (the chapter now has more than a hundred additional pages), adding new sections on:
• •Inverse limits of sets, Tag 01E3.
• •Direct colimits of sets, Tag 01F8.
• •The internal Hom of a powerset, Tag 01JT.
• •Isbell duality for sets (turned out to not be very interesting), Tag 01L1.
• •A six-functor formalism for (power)sets, Tag 01N1.
Additionally, the following sections have been substantially rewritten and/or had additional material added:
• •Unions of Families of Subsets, Tag 003E.
• •Intersections of Families of Subsets, Tag 003V.
• •Most subsections of Section: Operations With Sets.
• •All sections pertaining to powersets.
• •A new chapter, Chapter: Monoidal Structures on the Category of Sets, has been added.
• •Two new sections have been added to Chapter: Pointed Sets:
• •Subsection 01QC: Active and Inert Morphisms of Pointed Sets.
• •Subsection 01QS: Deleting Basepoints.
• •Corrected a mistake pointed out by Naïm Camille Favier in Item 01VL of Proposition 011T of Section 011R (and added them as a contributor — thank you so much, Naïm!). The corrected statement is now available as Tags 01U6 and 01U7.
• •Sligthly reorganized Chapter: Categories.
• •A new chapter, Chapter: Constructions With Monoidal Categories, has been added. It currently consists only of a single nonempty section, which is required for Tag 01P8.
• •Finally, a number of changes to the website infrastructure were implemented.

May 06

• •Initial release — yippee! 🥳