Introduction To Higher Order Categorical Logic

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

A short introduction ideal for students learning category theory for the first time.

This book illustrates linear logic in the application of proof theory to computer science.

A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.