We present preliminary work on a framework for constructing identities that takes as its point of departure Barwise’s channel theory, founded on category theory, and allied work on situation semantics. The framework takes actions relating to identity as fundamental. Actions and events are situations, although situations can include larger context. Identity-related situations are classified unde...

We consider (finitary, propositional) logics through the original use of Category Theory: the study of the “ sociology of mathematical objects”, aligning us with a recent, and growing, trend of study logics through its relations with other logics (e.g. process of combinations of logics as fibring [Gab] and possible translation semantics [Car]). So will be objects of study the classes of logics,...

We decribe the correspondence between normalised ω-operads in the sense of [1] and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category. Within the aforementioned correspondence, we provide also an equivalence between the algebras of a given normalised ωoperad, and categories enri...

The idea that vagueness has its origin in indiscernibility is not new. In this paper, we have tried to establish this thesis on a category-theoretic basis. In the process some other related notions, e.g. property, have been clari ed.

If you have taken a standard abstract algebra course, then you have probably heard of free groups. But, most such courses do not introduce the reader to the language of category theory, which unifies the notion of a free object. In the present lecture, we will define a free group categorically, and then go on to define a free module over a commutative ring, and hence, a free abelian group (whic...

There have traditionally been two approaches to modelling environments, one by use of nite products in Cartesian closed categories , the other by use of the base categories of indexed categories with structure. Recently, there have been more general deenitions along both of these lines: the rst generalising from Cartesian to symmetric premonoidal categories, the second generalising from indexed...

deleanu, frei, and hilton have developed the notion of generalized adams completion in a categorical context. in this paper, we have obtained the postnikov-like approximation of a module, with the help of a suitable set of morphisms.