[ nLab | product | Jocelyn Ireson-Paine's Home Page ]


This demonstration was written by Jocelyn Ireson-Paine to accompany the nLab page for product. It generates a categorical product of two sets and demonstrates its universality and non-uniqueness. It should work in any browser, and does not need Java or JavaScript.

To run it, press one of the buttons below. If you want, you can change the first button's input fields first. Leaving them as they are, or typing random, will generate a set at random. Typing randomne will generate a non-empty set at random. Typing a bracketed list of alphanumeric element names such as {a}, or {a,x}, or {x y}, or {foo,bar baz} will enter them as a set. To enter the empty set, just type {}.

Pressing the button will send a request to my Web server, which will return this page with a link in green at the top pointing to your results. Clicking this link will display these in a new browser window, or (depending on your browser) a new browser tab. If input checking detects an error such as a badly-formed set, it will report it in red.

The demonstration generates diagrams as well as text, and I'm happy for you to save and use any of the output. But the server soon deletes stuff to save space, so if you want to keep any output, grab it before it vanishes. You may redistribute it freely, but please acknowledge me.

Given the set X=
and the set Y=

This demonstration uses the same terminology as the corresponding nLab page. I have other interactive category theory demonstrations, not written to parallel nLab, here.