Introduction to Coalgebra: Towards Mathematics of States and Observation (Cambridge Tracts in Theoretical Computer Science)

The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists. 00. 9781107177895 01.0_pp_i_iv_Frontmatter 02.0_pp_v_vi_Contents 03.0_pp_vii_xvi_Preface 04.0_pp_1_32_Motivation 05.0_pp_33_113_Coalgebras_of_Polynomial_Functors 06.0_pp_114_158_Bisimulations 07.0_pp_159_245_Logic_Lifting_and_Finality 08.0_pp_246_333_Monads_Comonads_and_Distributive_Laws 09.0_pp_334_439_Invariants_and_Assertions 10.0_pp_440_465_References 11.0_pp_466_468_Definition_and_Symbol_Index 12.0_pp_469_477_Subject_Index