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Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develop theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model.To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory. ... Read more

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This book gives an account of the fundamental results in geometric stability theory, a subject that has grown out of categoricity theory and classification theory. This approach studies the fine structure of models of stable theories, using the geometry of forking; this often achieves global results relevant to classification theory. Topics range from Zilber-Cherlin classification of infinite locally finite homogenous geometries, to regular types, their geometries, and their role in superstable theories. The structure and existence of definable groups is featured prominently, as is work by Hrushovski. The book is unique in the range and depth of material covered and will be invaluable to anyone interested in modern model theory. ... Read more

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This book studies representable functors among well-known varieties of algebras. All such functors from associative rings over a fixed ring $R$ to each of the categories of abelian groups, associative rings, Lie rings, and to several others are determined. Results are also obtained on representable functors on varieties of groups, semigroups, commutative rings, and Lie algebras. The book includes a ``Symbol index'', which serves as a glossary of symbols used and a list of the pages where the topics so symbolized are treated, and a ``Word and phrase index''. The authors have strived--and succeeded--in creating a volume that is very user-friendly. ... Read more

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The goal of this work is to develop a functorial transfer of properties between a module $A$ and the category ${\mathcal M}_{E}$ of right modules over its endomorphism ring, $E$, that is more sensitive than the traditional starting point, $\textnormal{Hom}(A, \cdot )$. The main result is a factorization $\textnormal{q}_{A}\textnormal{t}_{A}$ of the left adjoint $\textnormal{T}_{A}$ of $\textnormal{Hom}(A, \cdot )$, where $\textnormal{t}_{A}$ is a category equivalence and $\textnormal{ q}_{A}$ is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right $E$-modules $\textnormal{Hom}(A,G)$, a connection between quasi-projective modules and flat modules, an extension of some recent work on endomorphism rings of $\Sigma$-quasi-projective modules, an extension of Fuller's Theorem, characterizations of several self-generating properties and injective properties, and a connection between $\Sigma$-self-generators and quasi-projective modules. ... Read more

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Over the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas.The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers.Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes.Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results. ... Read more

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This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $2ln$ of generic representations of $\textnormal{ SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($l \lt n$, first variable). A special case of this result yields the unramified computation and involves a new idea not presented before. This presentation, which contains detailed proofs of the results, is useful to specialists in automorphic forms, representation theory, and $L$-functions, as well as to those in other areas who wish to apply these results or use them in other cases. ... Read more

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A $G$-category is a category on which a group $G$ acts. This work studies the $2$-category $G$-Cat of $G$-categories, $G$-functors (functors which commute with the action of $G$ ) and $G$-natural transformations (natural transformations which commute with the $G$-action). There is particular emphasis on the relationship between a $G$-category and its stable subcategory, the largest sub-$G$-category on which $G$ operates trivially. Also contained here are some very general applications of the theory to various additive $G$-categories and to $G$-topoi. ... Read more

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This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales.The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories. ... Read more

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This book studies the universal constructions and properties in categories of commutative algebras, bringing out the specific properties that make commutative algebra and algebraic geometry work. Two universal constructions are presented and used here for the first time. The author shows that the concepts and constructions arising in commutative algebra and algebraic geometry are not bound so tightly to the absolute universe of rings, but possess a universality that is independent of them and can be interpreted in various categories of discourse. This brings new flexibility to classical commutative algebra and affords the possibility of extending the domain of validity and the application of the vast number of results obtained in classical commutative algebra. This innovative and original work will interest mathematicians in a range of specialities, including algebraists, categoricians, and algebraic geometers. ... Read more

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The book is an original treatise designed to defend an original, non-Aristotelian theory of categories. Chisholm argues that there are necessary things and contingent things; necessary things being things that are not capable of coming into being or passing away. He defends the argument from design, and thus includes the category of necessary substance (God).Further contentions of the essay are that attributes are also necessary beings, but not necessary substances, and that human beings are contingent substances but may not be material substances. ... Read more

Customer Reviews (1)

Not Chisholm's best work
This is the last book the excellent 20th century philosopher Roderick Chisholm wrote. It contains many of the final thoughts he had on metaphysical matters and for that reason is interesting. However, Chisholm was losing his sight by the time this book came about, and he wasn't able to edit it very well. Apparently he was a very visual writer and needed to see his thoughts written out to evaluate them and put them together coherently. This book jumps around a lot, even within chapters. Pieces of it are good on their own, but it doesn't fit together well, and substantive subject changes are frequent without any completion to the previous line of thought. It's probably worth reading for anyone who enjoys Chisholm's work. There's probably much benefit from such a pursuit. However, be aware of the deficiences of this book. ... Read more

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The two volumes of Architectural Theory bring together the fundamental elements of architecture and present them in a new and accessible format. The books define the areas of knowledge necessary for successful design and criticism and, for the first time in the history of architectural literature, integrate all the concepts to form a balanced and comprehensive whole. Volume One, A History of the Categories in Architecture and Philosophy, establishes the framework of architectural theory. The author presents a systematic analysis of what constitutes 'good' architecture in the West, tracing the history of architectural theory through the metaphysics of ancient Greece, the doctrines of early and medieval Christianity, up to the concepts and 'categories' of modern philosophy. The twentieth century has seen more building and more analysis of building than any other. Volume Two, Principles of Twentieth-century Architectural Theory Arranged by Category, focuses on the recent fragmentation of architectural theory into distinct doctrines. Formalism, minimalism, mannerism, functionalism, rationalism, brutalism, positivism, romanticism, expressionism, classicism, constructivism, organicism, modernism, futurism, radicalism, deconstructivisim, historicism, post-modernism - each movement has influenced the shape of architectural thinking over the last century. Principles of Twentieth-century Architectural Theory Arranged by Category analyses each in turn and places each in context. The volumes are liberally illustrated with representative buildings of the period and include a glossary of terms, a thesaurus, an annotated guide to further reading as well as diagrammatic links connecting themes across both volumes. The two volumes, whether studied together or individually, will prove invaluable to students of architecture and related disciplines. ... Read more

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The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories, this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions. ... Read more

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The scientific approach of this book transcends the limits of art literature in that it also develops geometric theories of gestures and distributed identities, also known as swarm intelligence.

We exemplify this approach in the framework of free jazz, which is a prototypical creative and collaborative art form. Leader artists such as John Coltrane, Pharoah Sanders, Cecil Taylor, Sun Ra, The Art Ensemble of Chicago, Albert Ayler, Don Cherry, and Archie Shepp are presented in their strongest works and theories. A CD with new recordings of the group Tetrade (Jeff Kaiser on trumpet, Guerino Mazzola on piano, Sirone on bass, Heinz Geisser on percussion) is included.

The pillars of our theory of collaboration are built from psychologist Mihaly Csikszentmihalyi’s flow, physicist Gilles Châtelet’s gestures, and computer scientist Bill Wulf's collaboratories.