## 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...

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...

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...

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...

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...

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...

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 ...

In my previous post “Category theory notes 17: Reflective subcategory (Part 1)” I discussed the similarity and distinction between linguistic and mathematica...

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...

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...

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...

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...

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...

So, after reading many textbooks, watching many video tutorials, and attending two guided courses, I finally understood adjunction. That was a real “Eureka!”...

In my previous post “Category theory notes 10: Composite naturality (Part 1)” I illustrated the vertical and horizontal compositions of natural transformatio...

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 textbooks often warn learners that categorical objects and arrows shouldn’t be tied to sets and functions. A poset category, for example, has...

Fong & Spivak refer to category, functor, and natural transformation as the “big three” of category theory in their newly published textbook An Invitatio...

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 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....

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...

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 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...

The term category is anything but unfamiliar to linguisticians. Human language is all about categories. For example, speech sounds are grouped into various n...

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 ...