There are two main approaches to obtaining \topological" cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed | for example, the category of sequential spaces. Under the other, one generalises the notion of space | for example, to Scott's notion of equilogical space. In this paper we show that the two appr...

We give a complete and careful proof of Quillen’s theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories.

In categories related to complete quasi-monoidal lattices, we investigate the relations among (L,♦)-(respectively, (L, )-,(L, )-) fuzzy quasi-uniform spaces, (L, ,∧)-fuzzy topological spaces and (L, ,∧)fuzzy interior spaces induced functions. Mathematics Subject Classification: 54A40, 08A72, 06D72

Motivated by research on how topology may be a helpful foundation for building information modeling (BIM), a relational database version of the notions of chain complex and chain complex morphism is defined and used for storing cw-complexes and their morphisms, hence instances of building projects and different views upon them, into relational databases. In many cases, this can be done without ...

A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...

Every homology or cohomology theory on a category ofE∞ ring spectra is Topological André–Quillen homology or cohomology with appropriate coefficients. Analogous results hold more generally for categories of algebras over operads. Mathematics Subject Classification (2000): 55P43, 55P48, 55U35

1 Topological Field Theories and Higher Categories 2 1.1 Classical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Extending Down: Lower Dimensional Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Higher Category Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Extending Up: Diffeo...

1 Topological Field Theories and Higher Categories 2 1.1 Classical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Extending Down: Lower Dimensional Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Higher Category Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Extending Up: Diffeo...

A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...

the influence of cation-π interactions on the strength and nature of intramolecular o...h hydrogen bond has been investigated by quantum chemical calculations in orthohydroxy benzaldehyde (hba) compound. ab initio calculations have been performed at mp2/6-311++g** level of theory. vibrational frequencies and physical properties such as chemical potential and chemical hardness of these compounds...