Changes

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

2024

December 04

• Revised and added new material on moduli of monoidal structures to Chapter 10: 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 4: 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 2: 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 01JS.
• Isbell duality for sets (turned out to not be very interesting), Tag 01L0.
• A six-functor formalism for (power)sets, Tag 01MY.
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 2.3: Operations With Sets.
• All sections pertaining to powersets.
• A new chapter, Chapter 3: Monoidal Structures on the Category of Sets, has been added.
• Two new sections have been added to Chapter 4: Pointed Sets:
• Subsection 4.1.5: Active and Inert Morphisms of Pointed Sets.
• Subsection 4.4.2: Deleting Basepoints.
• Corrected a mistake pointed out by Naïm Camille Favier in Item 1 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 01YB and 01YC.
• Sligthly reorganized Chapter 15: Categories.
• A new chapter, Chapter 10: 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! 🥳