One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable ...

Quite a number of models have been proposed under the name of structured analysis and design. It has been pointed out, however, that there is no common theoretical framework among them. Transformation of a specification from one model to another, although often recommended by authors, can only be done manually. A category-theoretic approach is proposed in this paper. As a result, development of...

Formal software speciication has long been touted as a way to increase the quality and reliability of software; however, it remains an intricate, manually intensive activity. An alternative to using formal speciications directly is to translate graphically-based, semi-formal speciications into formal speciications. However, before this translation can take place, a formal deenition of basic obj...

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In this lecture I will discuss a very nice unifying principle for a number of topics in enumerative combinatorics, the theory of species, introduced by André Joyal in 1981. Species have been used in areas ranging from infinite permutation groups to statistical mechanics, and I can’t do more here than barely scratch the surface. Joyal gave a category-theoretic definition of species; I will take ...

Quasi-categories live at the intersection of homotopy theory with category theory. In particular, they serve as a model for (∞, 1)-categories, that is, weak higher categories with n-cells for each natural number n that are invertible when n > 1. Alternatively, an (∞, 1)-category is a category enriched in ∞-groupoids, e.g., a topological space with points as 0-cells, paths as 1-cells, homotopies...

We show that entropic varieties provide the canonical setting for a generaliziation of Hopf algebra theory. In particular we show that all naturally occurring functors in this context have the expected adjoints, when generalized to this level. In particular, universal measuring comonoids exist over every entropic variety, as do generalized group algebras, and these carry a canonical Hopf struct...

Motivated by examples from general relativity and Newtonian gravitation, this essay attempts to distinguish between the dynamical structure associated with a theory in physics, and its kinematical structure. This enables a distinction to be made between a structural realist interpretation of a theory based on its dynamical structure, and a structural realist interpretation of spacetime, as desc...