the category whose objects aremorphisms of fine saturated log schemes Y log → X , where Y is a noetherian scheme, and the underlying morphism of schemes Y → X is of finite type, and whose morphisms (from an object Y log 1 → X log to an object Y log 2 → X ) are morphisms of finite type Y log 1 → Y log 2 (i.e., morphisms for which the underlying morphism of schemes Y1 → Y2 is of finite type) lyin...

A Diagrammatic Category for the Representation Theory of Uq(sln) by Scott Edward Morrison Doctor of Philosophy in Mathematics University of California, Berkeley Professor Vaughan Jones, Chair This thesis provides a partial answer to a question posed by Greg Kuperberg in [24] and again by Justin Roberts as problem 12.18 in Problems on invariants of knots and 3-manifolds [28], essentially: Canwe ...

A Diagrammatic Category for the Representation Theory of U q (sl n) This thesis provides a partial answer to a question posed by Greg Kuperberg in [24] and again by Justin Roberts as problem 12.18 in Problems on invariants of knots and 3-manifolds [28], essentially: Can one describe the category of representations of the quantum group U q (sl n) (thought of as a spherical category) via generato...

After defining, for each many-sorted signature Σ = (S,Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for TΣ, the monad in Set determined by the adjunctionTΣ ⊣ GΣ from Set toAlg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor d⋄ from Ter(Σ) to Ter(Λ). Once defined the mappings that assign, respectively...

One of the main notions in category theory is the notion of limit. Similarly, one of the most commonly used techniques in homotopy theory is the notion of “homotopy limit” commonly called “holim” for short. The purpose of the this paper is to begin to develop the notion of limit for n-categories, which should be a bridge between the categorical notion of limit and the homotopical notion of holi...

The main purpose of this work is to find not canonical equivalence category and morphism diffeomorphism from smooth manifold with Fundemental Fibre Bundle denoted by groupoids P.

A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent.

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show a ^n$-manifold (resp., ^n$-morphism) can be reconstructed from its algebra global ^n$-functions morphism between ^n$-function algebras). These results are importance in study ^n$ Lie groups. The investigation is more challenging, since completed tensor product structure sheafs two not sheaf. rely...

The category-theoretic nature of general frames for modal logic is explored. A new notion of “modal map” between frames is defined, generalizing the usual notion of bounded morphism/p-morphism. The category Fm of all frames and modal maps has reflective subcategories CHFm of compact Hausdorff frames, DFm of descriptive frames, and UEFm of ultrafilter enlargements of frames. All three subcategor...

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...