ACT2022 conference notes: Linguistics
In the previous post, I introduced my submission to the 2022 Applied Category Theory conference (ACT2022). Now that the conference is over, I’d like to share...
mathematics
Another application of category theory in linguistics (Part 2)
[Link to Part 1 of this post]
Another application of category theory in linguistics (Part 1)
This post is part of my portfolio for the poster session at the Applied Category Theory 2022 conference (ACT2022). It is a gentle introduction to my applicat...
ACT2020 conference notes: Main sessions
In the previous four posts I organized my notes from the ACT2020 Tutorial Day. In this post I’ll continue to note down things I’ve learned from the main sess...
ACT2020 conference notes: Tutorial Day Lecture 1 (David Spivak)
So I’m participating in this year’s Applied Category Theory conference (with a virtual poster—check it out here!), and the preconference Tutorial Day has jus...
A new application of category theory in linguistics (part 2)
In the previous post I laid out the disciplinary background of my application of category theory in linguistics in more detail (than I had done in my explain...
A new application of category theory in linguistics (part 1)
This is the second part of my “portfolio” prepared for the virtual poster session at ACT2020. It introduces my category-theoretic modeling of the human langu...
Category theory notes 20: Category theory for posets (Part 2)
In my previous post “Category theory notes 19: Category theory for posets (Part 1)” I began writing about the “poset versions” of some category-theoretic res...
Category theory notes 19: Category theory for posets (Part 1)
Throughout this blog series I’ve been writing about category-theoretic results in their fully general forms, which are applicable to all categories from all ...
Category theory notes 18: Reflective subcategory (Part 2)
In my previous post “Category theory notes 17: Reflective subcategory (Part 1)” I discussed the similarity and distinction between linguistic and mathematica...
Category theory notes 17: Reflective subcategory (Part 1)
So far in this series I’ve viewed a category as an individual and independent entity. Two categories may be related by functors or even better connected by a...
Category theory notes 16: Yoneda lemma (Part 3)
In the previous two posts, “Category theory notes 14: Yoneda lemma (Part 1)” and “Category theory notes 15: Yoneda lemma (Part 2),” I started a task of decip...
Category theory notes 15: Yoneda lemma (Part 2)
In the previous post “Category theory notes 14: Yoneda lemma (Part 1)” I began writing about IMHO the most challenging part in basic category theory, the Yon...
Category theory notes 14: Yoneda lemma (Part 1)
Awodey calls it “the single most used result” of category theory (Category Theory, p. 185), Crole regards it as “an indispensable tool which every category t...
Category theory notes 13: Adjunction (Part 2)
In the previous post “Category theory notes 12: Adjunction (Part 1)” I wrote about my thoughts on adjunction, an extremely important component of category th...
Category theory notes 12: Adjunction (Part 1)
So, after reading many textbooks, watching many video tutorials, and attending two guided courses, I finally understood adjunction. That was a real “Eureka!”...
Category theory notes 11: Composite naturality (Part 2)
In my previous post “Category theory notes 10: Composite naturality (Part 1)” I illustrated the vertical and horizontal compositions of natural transformatio...
Category theory notes 10: Composite naturality (Part 1)
The notion of natural transformation is surprisingly easy to follow. If you know what an arrow is and what a functor is, then you automatically know what a n...
Category theory notes 9: Full and half inverses
Category theory textbooks often warn learners that categorical objects and arrows shouldn’t be tied to sets and functions. A poset category, for example, has...
Category theory notes 8: Functoriality
Fong & Spivak refer to category, functor, and natural transformation as the “big three” of category theory in their newly published textbook An Invitatio...
Category theory notes 7: Categorical idioms
Idioms and slangs are an important part of human language. They are short, expressive, and vividly reflect regional/historical mind-sets. And they are usuall...
Category theory notes 6: Think big
Category theory is spectacularly big. But exactly how big is it? Consider a set $A$. It can hold a huge number of elements, say, all grains of sand on Earth....
Category theory notes 5: Arrows and diagrams
Arrows are so vital to category theory that Awodey jokingly refers to the theory as “archery” (Category Theory, p. 2). Given two objects in a category, an ar...
Category theory notes 4: Monoid
Monoid is one of those concepts that are extremely simple, extremely useful, and can at the same time be extremely confusing. It was one of the first concept...
Category theory notes 3: Categorial or categorical?
Category in category theory is a noun, but we often need to use the term in other parts of speech (notably adjective and verb). Try the following quiz for ex...
Category theory notes 2: What’s a category?
The term category is anything but unfamiliar to linguisticians. Human language is all about categories. For example, speech sounds are grouped into various n...
Category theory notes 1: A linguistician’s babble
So I ended up using category theory in my linguistics dissertation. How this happened is a long story. Basically I stumbled into a promising-looking toolkit ...