Accessible aspects of 2-category theory

Modeling Aspects by Category Theory

A framework for formal analysis of aspect-oriented software development (AOSD) is proposed. AOSD is treated as enriching formal models of programs by traceable refinements that produce their systemic interfaces. Category-theoretic construction of architecture school is employed to formalize this approach. Aspect weaving and separation of concerns are defined as universal constructions. Aspect-o...

Two Constructivist Aspects of Category Theory

Category theory has two unexpected links to constructivism: First, why is topos logic so close to intuitionistic logic? The paper argues that in part the resemblance is superficial, in part it is due to selective attention, and in part topos theory is objectively tied to the motives for later intuitionistic logic little related to Brouwer’s own stated motives. Second, why is so much of general ...

The 2-category theory of quasi-categories

In this paper we re-develop the foundations of the category theory of quasicategories (also called ∞-categories) using 2-category theory. We show that Joyal’s strict 2-category of quasi-categories admits certain weak 2-limits, among them weak comma objects. We use these comma quasi-categories to encode universal properties relevant to limits, colimits, and adjunctions and prove the expected the...

T-monoids and 2-dimensional Category Theory

Category Theory

This article presents a development of Category Theory in Isabelle. A Category is defined using records and locales in Isabelle/HOL. Functors and Natural Transformations are also defined. The main result that has been formalized is that the Yoneda functor is a full and faithful embedding. We also formalize the completeness of many sorted monadic equational logic. Extensive use is made of the HO...