Thesis--University of Florida. / Manuscript copy. Vita. Description based on print version record. Bibliography: leaf 67.

Thesis--University of Florida. / Description based on print version record. Manuscript copy. Vita. Bibliography: leaf 60.

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Thesis (M.A.)--University of Montana, 2008. / Title from title screen. Description based on contents viewed Aug. 21, 2008. Includes bibliographical references (p. 78-79).

The contribution of this thesis is a novel framework for rewriting in higher categories. Its theoretical foundation is the theory of quasistrict higher categories and the practical realisation is a proof assistant Globular. The framework introduces the notions of diagrams and signatures as new mutually-recursive structures that give the algebraic basis for the approach. These structures are related the notion of an n-polygraph, but allow reasoning about quasistrict higher categorical structures in a way amenable to computer implementation. Building on this, we propose a new definition of a quasistrict 4-category, and prove a result that in a quasistrict 4-category, an adjunction of 1-morphisms gives rise to a coherent adjunction satisfying the butterfly equations.

For each abelian category A, there is a category D(A), called the derived category of A, whose objects are complexes of objects of A, and whose morphisms are formal fractions of homotopy classes of complex morphisms having as denominators homotopy classes inducing isomorphisms in cohomology. If F : A →B is an additive functor between abelian categories, then under suitable conditions on A, there is a functor RF : D(A) → D(B) with the property that if objects X of A are considered as complexes concentrated at degree 0, then there are isomorphisms [formula omitted] for all n, where [formula omitted] is the ordinary [formula omitted] right derived functor of F. RF is called the derived functor of F, and one may look upon it as a kind of extension of F. / Science, Faculty of / Mathematics, Department of / Graduate

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