A Gentle Introduction to Category Theory: the calculational approach
by Maarten M. Fokkinga
Publisher: University of Twente 1994
Number of pages: 80
In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. This text differs from most other introductions to category theory in the calculational style of the proofs, the restriction to applications within algorithmics, and the omission of many additional concepts and facts that I consider not helpful in a first introduction to category theory.
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by Emily Riehl - Dover Publications
This is a concise, original text for a one-semester introduction to the subject. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, monads, etc.
by J. Cigler, V. Losert, P.W. Michor - Marcel Dekker Inc
This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.
by Michael Barr, Charles Wells
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
by Brendan Fong, David I Spivak - arXiv.org
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.