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Webpage of the Compositional Systems and Methods group at TalTech.

Introduction to Category Theory and its applications

When

First lecture: Jan 31, 2022 @ 10am EET

Where

Monday : ICT building room A1
Friday : ICT building probably the coffee room in kybi

How

We meet in person, we are sick of the pandemic.

Who

Pawel Sobociński
Fosco Loregian

What

An introductory course on category theory and its applications.

Good references for studying category theory are:

Riehl "Category theory in context"
Leinster "Basic Category Theory"
Borceux "Handbook of categorical algebra", vol 1-3
Mac Lane, "Categories for the working mathematician"
Awodey "Category theory"
Barr & Wells "Category Theory for Computing Science"

If your plan is to end this course knowing strictly more than the teachers, the (delightful) "Practical Foundations of Mathematics" by Paul Taylor follows a philosophy very similar to the one we're taking. This similarity wasn't engineered on purpose.

Chapter I is a swift introduction to the foundation of Mathematics; Chapter II is a crash course on "set theory", where both the word "set" and the word "theory" acquire a better meaning than in other books. Chapter III deals with order structures, but it's constantly, and not so secretly, talking about category theory.

Why

Because category theory = {cool stuff} ∩ {useful stuff}!

Lectures

On posets | PDF

On monoids | PDF

Exercises

here a HIGHLY UNSTABLE draft


Victor Brauner, Arche-chat, 1948, Herbert F. Johnson Museum of Art (Cornell University), Ithaca, NY, US.