## June 29, 2019

### Behavioral Mereology

#### Posted by John Baez

*guest post by Toby Smithe and Bruno Gavranović*

What do human beings, large corporations, biological cells, and gliders from Conway’s Game of Life have in common?

This week in the Applied Category Theory
School,
we attempt some first steps towards answering this
question. We turn our attention to
autopoiesis,
the ill-understood phenomenon of self-perpetuation that
characterizes life. Our starting point is Behavioral
Mereology, a new take on
the ancient question of parthood: how should we understand
the relationship between a part and a whole? The authors
Fong, Myers, and Spivak suggest that we cleave a whole into
parts by observing – and grouping together — regularities
in its behavior. Parthood entails behavioral constraints,
which are mediated by the whole. We describe the
corresponding logic of constraint passing, and the
associated modalities of *compatibility* and *ensurance*. We
propose that autopoiesis entails a special kind of parthood
— one that ensures its compatibility with its environment
— and end with a list of open questions and potential
research directions.

## June 25, 2019

### Meeting the Dialogue Challenge

#### Posted by John Baez

*guest post by Dan Shiebler and Alexis Toumi*

This is the fourth post in a series from the Adjoint School of Applied Category Theory 2019. We discuss Grammars as Parsers: Meeting the Dialogue Challenge (2006) by Matthew Purver, Ronnie Cann and Ruth Kempson as part of a group project on categorical methods for natural language dialogue.

## June 20, 2019

### Katrina Honigs meets Grothendieck

#### Posted by John Baez

Here’s a fun story by Katrina Honigs about how she found Grothendieck’s house in the Pyrenees, jumped the fence, knocked on the door, and offered him some pastries.

## June 16, 2019

### Applied Category Theory Meeting at UCR

#### Posted by John Baez

The American Mathematical Society is having their Fall Western meeting here at U. C. Riverside during the weekend of November 9th and 10th, 2019. Joe Moeller and I are organizing a session on Applied Category Theory!

## June 13, 2019

### What’s a One-Object Sesquicategory?

#### Posted by John Baez

A **sesquicategory**, or $1\frac{1}{2}$-category, is like a 2-category, but without the interchange law relating vertical and horizontal composition of 2-morphisms:

$(\alpha \cdot \beta)(\gamma \cdot \delta) = (\alpha \gamma) \cdot (\beta \delta)$

Better, sesquicategories are categories enriched over $(Cat,\square)$: the category of categories with its “white” tensor product. In the *cartesian* product of categories $C$ and $D$, namely $C \times D$, we have the law

and we can define $f \times g$ to be either of these. In the *white* tensor product $C \square D$ we do not have this law, and $f \times g$ makes no sense.

What’s a one-object sesquicategory?

## June 5, 2019

### Nonstandard Models of Arithmetic

#### Posted by John Baez

A nice quote:

There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time.

This is from Matthew Katz and Jan Reimann’s nice little book *An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics*. I’ve been been talking to my old friend Michael Weiss about nonstandard models of Peano arithmetic on his blog. We just got into a bit of Ramsey theory. But you might like the whole series of conversations.

## June 3, 2019

### Why Category Theory Matters

#### Posted by John Baez

No, I’m not going to tell you why category theory matters. To learn that, you must go here:

- Robb Seaton, Why category theory matters, rs.io.