The joy of abstraction : an exploration of math, category theory, and life

Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background--Publisher's description 00. 9781108477222 01.0_pp_i_vi_Frontmatter 02.0_pp_vii_viii_Dedication 03.0_pp_ix_xiv_Contents 04.0_pp_1_10_Prologue 05.0_pp_11_12_Building_up_to_Categories 05.1_pp_13_22_Categories_the_idea 05.2_pp_23_34_Abstraction 05.3_pp_35_43_Patterns 05.4_pp_44_51_Context 05.5_pp_52_66_Relationships 05.6_pp_67_81_Formalism 05.7_pp_82_94_Equivalence_relations 05.8_pp_95_108_Categories_the_definition 06.0_pp_109_110_A_Tour_of_Math 06.1_pp_111_116_Examples_weve_already_seen_secretly 06.2_pp_117_123_Ordered_sets 06.3_pp_124_135_Small_mathematical_structures 06.4_pp_136_145_Sets_and_functions 06.5_pp_146_162_Large_worlds_of_mathematical_structures 07.0_pp_163_164_Doing_Category_Theory 07.1_pp_165_185_Isomorphisms 07.2_pp_186_205_Monics_and_epics 07.3_pp_206_225_Universal_properties 07.4_pp_226_236_Duality 07.5_pp_237_269_Products_and_coproducts 07.6_pp_270_289_Pullbacks_and_pushouts 07.7_pp_290_308_Functors 07.8_pp_309_327_Categories_of_categories 07.9_pp_328_350_Natural_transformations 07.10_pp_351_367_Yoneda 07.11_pp_368_395_Higher_dimensions 08.0_pp_396_400_Thinking_categorically 09.0_pp_401_402_Appendices 09.1_pp_403_403_Background_on_alphabets 09.2_pp_404_404_Background_on_basic_logic 09.3_pp_405_406_Background_on_set_theory 09.4_pp_407_409_Background_on_topological_spaces 10.0_pp_410_415_Glossary 11.0_pp_416_417_Further_Reading 12.0_pp_418_419_Acknowledgements 13.0_pp_420_424_Index Journey through the world of abstract mathematics into category theory with popular science author Eugenia Cheng. Featuring humanizing examples and demystification of mathematical thought processes, this book is for fans of How to Bake Pi who want to dig deeper into mathematical concepts and build their mathematical background.