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Ruby Khondaker (she/her) (Jan 10 2026 at 21:59):Published a blog post collecting together my thoughts regarding "Indexed-Fibred Duality", which I first started considering back in #learning: questions > ✔ Comma Categories vs Categories of Elements.
Rémy Tuyéras (Jan 10 2026 at 22:10):Looks great. Maybe you could give it an introduction with a short description of what the reader can/will learn from it
Ruby Khondaker (she/her) (Jan 10 2026 at 22:55):Thank you - I suppose the main goal of the post is to give some intuition for “fibrations”, which was one of the topics I was confused about for quite a long time.
Alex Kreitzberg (Jan 10 2026 at 23:08):Nice article, thanks for writing it!
Alex Kreitzberg (Jan 11 2026 at 01:45):Also thank you for citing "Categorical Logic and Type Theory", that book looks interesting.
Ruby Khondaker (she/her) (Jan 11 2026 at 15:01):A quick follow-up article to my last post, explaining how to apply Indexed-Fibred duality to defining Infinitary Cartesian Products.
Ruby Khondaker (she/her) (Jan 18 2026 at 18:58):Hey y’all, this article has been a long time coming - my explanation of categorical products! Instead of the usual definition with projections, I prefer thinking about them as categorical “packagers”. Enjoy :)
https://pseudonium.github.io/2026/01/18/Products_Categorically.html
Peva Blanchard (Jan 18 2026 at 21:45):Ruby Khondaker (she/her) said:
Hey y’all, this article has been a long time coming - my explanation of categorical products! Instead of the usual definition with projections, I prefer thinking about them as categorical “packagers”. Enjoy :)
https://pseudonium.github.io/2026/01/18/Products_Categorically.html
Interesting. Just to check if I got the metaphor right: would you think of a representing object (for some presheaf ) as a "packager" of -data?
Ruby Khondaker (she/her) (Jan 18 2026 at 22:01):Yes, that’s the sort of intuition I have. For example, I like to think of limits and colimits as packaging an entire diagram into a single object, such that maps into the limit represent “maps into the diagram”, I.e. cones over the diagram, and dually for colimits. You compress F-data into a single morphism.
Ruby Khondaker (she/her) (Jan 19 2026 at 14:25):Update - I added lots of diagrams to the post to make it easier to follow, and also to illustrate how this links to the usual formulation of the product's universal property.
Ruby Khondaker (she/her) (Jan 22 2026 at 19:44):Another post I've been cooking up for quite a while - the "Baby Yoneda Lemma"! It's a simpler version of Yoneda that still contains most of its essence, which I've tried to explain in as clear a way as I can. I hope this helps to dispel some of the confusion and mystery surrounding the fundamental theorem of category theory :)
https://pseudonium.github.io/2026/01/22/The_Baby_Yoneda_Lemma.html
Ruby Khondaker (she/her) (Jan 26 2026 at 17:45):Hey y'all, I've got another article for you in the "Baby Yoneda" series! This one focuses on the notion of _representing_ virtual objects by actual objects.
https://pseudonium.github.io/2026/01/26/Baby_Yoneda_2_Representable_Boogaloo.html