{"content":[{"text":"X","bbox":{"left":0.075711,"top":0.057372,"width":0.010549000000000003,"height":0.017615}},{"text":"PREFACE","bbox":{"left":0.433943,"top":0.057696,"width":0.09988599999999997,"height":0.016033999999999993}},{"text":"As to the specific treatment of category theory, I have attempted to \n play down the functorial perspective initially and take an elementary (in \n the sense of “first-order”) approach, using the same kind of combinatorial \n manipulation of algebraic structure that is employed in developing the \n basic theory of any of the more familiar objects of pure-mathematical \n study. In these terms categories as structures are no more rarified than \n groups, lattices, vector-spaces etc. \n I should explain that whereas the bulk of the manuscript was completed \n around May of 1977, the sections 11.9, 14.7 and 14.8 were written a year \n later while I was on leave in Oxford (during which time I held a \n Travelling Fellowship from the Nuffield Foundation, whose assistance I \n am pleased to acknowledge). The additional material was simply ap­ \n pended to Chapters 11 and 14, since, although the arrangement is less \n than ideal, it was impractical at that stage to begin a major reorganisa­ \n tion. I imagine however that there will be readers interested in the \n construction of number-systems in 14.8 who do not wish to wade through \n the earlier material in Chapter 14 on Grothendieck topologies, elemen­ \n tary sites etc. In fact in order to follow the definition of Dedekind-reals in \n the topos of 12-sets, and their representation as classical continuous \n real-valued functions, it would suffice to have absorbed the description of \n that topos given in 11.9. The full sheaf-theoretic version of this construc­ \n tion depends on the theory of Ω -sheaves developed in 14.7, but a \n sufficient further preparation for the latter would be to read the first few \n pages of 14.1, at least as far as the introduction of the axiom COM on \n page 362. \n A point of terminology: - 1 have consistently used the word “ categor- \n ial” where the literature uniformly employs “ categorical” . The reason is \n that while both can serve as adjectival forms of the noun “ category” , the \n second of them already has a different and long established usage in the \n domain of logic, one that derives from its ordinary-language meaning of \n “ absolute” . Logicians have known since the work of Godel that set \n theory has no categorical axiomatisation. One function of this book will \n be to explain to them why it does have a categorial one.","bbox":{"left":0.073425,"top":0.090539,"width":0.822611,"height":0.681847}},{"text":"There are a number of people who I would like to thank for their help \n in the production of the book. I am indebted to Shelley Carlyle for her \n skilful typing of the manuscript; to the Internal Research Committee and \n the Mathematics Department of the Victoria University of Wellington for \n substantially subsidising its cost; to Pat Suppes for responding favourably \n to it, and supporting it; and to Einar Fredriksson and Thomas van den","bbox":{"left":0.076219,"top":0.795026,"width":0.8197509999999999,"height":0.12367499999999998}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}