This book provides a gentle, software engineering oriented introduction to category theory. Assuming only a minimum of mathematical preparation, this book explores the use of categorical constructions from the point of view of the methods and techniques that have been proposed for the engineering of complex software systems:risk analysis. Risk analysis is one of the main parts of complex systematic research of natural and man-made hazards and risks together with concepts of Risk Analysis, Risk Management, Acceptable Risk and Risk Reduction.Risk Analysis is considered as the process of making a recommen dation on whether existing risks are acceptable and present risk control measures are adequate, and if they are not, whether alternative risk control measures are justified or will be implemented.