Category theory is well-known for abstraction—concepts and tools from diverse fields being recognized as specific cases of more foundational structures—though the field has always been driven and shaped by the needs of applications. Moreover, category theory is rarely introduced even to undergraduate math majors, despite its unifying role in theory and its flexibility in application.

Postdoctoral Associate Brendan Fong and Research Scientist David I. Spivak, both at MIT, have written a marvelous and timely new textbook that, as its title suggests, invites readers of all backgrounds to explore what it means to take a compositional approach and how it might serve their needs.

An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Cambridge University Press, 2019) has few mathematical prerequisites and is designed in part as a gateway to a wide range of more specialized fields. It also centers its treatment on applications, motivating several key developments in terms of real-world use cases.

In this interview we discussed their views on the promise of category theory inside and outside mathematics, their motivations for writing this book, several of the accessible examples and remarkable payoffs included in its chapters, and their aspirations for the future of the field.

Suggested companion works:

--Tai-Danae Bradley, Math3ma

--Eugenia Cheng, The Catsters

--Saunders Mac Lane, Mathematics Form and Function

--F. William Lawvere & Stephen H. Schanuel, Conceptual Mathematics: A First Introduction to Categories

--Eugenia Cheng, x + y: A Mathematician's Manifesto for Rethinking Gender

Cory Brunson (he/him) is a Research Assistant Professor in the Laboratory for Systems Medicine at the University of Florida.

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