Preface. Contents. Preliminaries. Prospectus. Logic, ty pe theory, and fibred category theory. The logic and type theory of sets . Introduction to fibred category theory. Fibrations. S ome concrete examples: sets, &ohgr;-sets and PERs. Some general examples . Cloven and split fibrations. Change-of-base and composition for fibrat ions. Fibrations of signatures. Categories of fibrations. Fibrewise stru cture and fibred adjunctions. Fibred products and coproducts. Indexed ca tegories. Simple type theory. The basic calculus of typ es and terms. Functorial semantics. Exponents, products and coproducts. Semantics of simple type theories. Semantics of the untyped lambda calcu lus as a corollary. Simple parameters. Equational logic. Logics. Specifications and theories in equational logic. Algebraic spe cifications. Fibred equality. Fibrations for equational logic. Fibred fu nctorial semantics. First order predicate logic. Signat ures, connectives and quantifiers. Fibrations for the first order predic ate logic. Functorial interpretation and internal language. Subobject fi
Preface. Contents. Preliminaries. Prospectus. Logic, ty pe theory, and fibred category theory. The logic and type theory of sets . Introduction to fibred category theory. Fibrations. S ome concrete examples: sets, &ohgr;-sets and PERs. Some general examples . Cloven and split fibrations. Change-of-base and composition for fibrat ions. Fibrations of signatures. Categories of fibrations. Fibrewise stru cture and fibred adjunctions. Fibred products and coproducts. Indexed ca tegories. Simple type theory. The basic calculus of typ es and terms. Functorial semantics. Exponents, products and coproducts. Semantics of simple type theories. Semantics of the untyped lambda calcu lus as a corollary. Simple parameters. Equational logic. Logics. Specifications and theories in equational logic. Algebraic spe cifications. Fibred equality. Fibrations for equational logic. Fibred fu nctorial semantics. First order predicate logic. Signat ures, connectives and quantifiers. Fibrations for the first order predic ate logic. Functorial interpretation and internal language. Subobject fi
Chapter Headings only. Preface. Contents. Preliminaries. Prospectus. Introduction to fibred category theory. Simple type theory. Equational logic. First order predicate logic. Higher order predicate logic. The effective topos. Internal category theory. Polymorphic type theory. Advanced fibred category theory. First order dependent type theory. Higher order dependent type theory. References. Notation index. Subject index.
"The author's achievement in collecting and organizing a very large body of material in coherent form,... this is first and foremost an encyclopaedic work, into which specialists will delve with much pleasure and profit... One very welcome feature of the book is a comprehensive bibliography of nearly 350 items..." --Zentralblatt für Mathematik, vol.905R.A.G. Seely"This book will be the standard reference in its field for some time to come." --The Bulletin of Symbolic Logic, Vol. 6
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