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“Try as you may,

you just can’t get away,

from mathematics”

Tom Lehrer

About this book

This book is a product of my own endeavour of understanding category theory. It is just that as I am explaining something, I am understanding it better. It is aimed at programmers, as well as anyone else who is interested in this stuff.

The main reason I am interested in category theory is that it allows us to formalise some common concepts that we use in our daily (intellectual) lives. Much of our language is based on intuition and rightfully so: relying on intuition is a very easy way to get your point across so it is understood by other human beings. However, that is part of the problem: sometimes intuition makes it too easy to communicate with someone. So easy that he might, in fact, understand things that you haven’t actually said. For example, when I say that two things are equal, it would seem obvious to you what I mean, although it isn’t obvious at all (how are they equal, at what context etc). That is the place when we might want to provide a more rigorous definition of what am I saying (even if I did not have one to begin with). But providing such definition in natural language, which is designed to use intuition as a means of communication, is no easy task.

It is in these situations that people often resort to diagrams to explain their thoughts. Diagrams are ubiquitous in science and mathematics because they are an understandable way to communicate a formal concept clearly. Category theory formalises the concept of a diagram and their components - arrows and objects and creates a language for presenting all kinds of ideas.

In this book, we will visit those formalisms and along the way, we would see all other kinds of mathematical objects, viewed under the prism of categories.

Acknowledgements

Thanks to my wife Dimitrina, who has no issue with taking after our daughter while I sit here and write my book.

Thanks to my high-school arts teacher, Mrs Georgieva who told me that I have some tallent, but I have to actually work to make it happen.

Thanks to Prathyush Pramod who encouraged me to finish the book and is also helping me out with it.

And also to everyone else who submitted feedback and helped me fix some of the numerous errors that I made - knowing myself, I know that there are a lot more.

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