Categories without Structures

Categories without structures

Categories of relational structures

The paper characterises compositional homomorphims of relational structures. A detailed study of three categories of such structures { viewed as multialgebras { reveals the one with the most desirable properties. In addition, we study analogous categories with homomorphisms mapping elements to sets (thus being relations). Finally, we indicate some consequences of our results for partial algebra...

Triangulated categories without models

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not admit any non-trivial exact functors to or from these algebraic respectively topological triangulated categories. Introduction. Triangulated categories are ...

Syntax without functional categories

This paper argues against the notion 'functional category' (a kind of word-class) while accepting that individual words may be described as 'function' words or 'content' words. It focuses on the two least controversial examples of functional categories — 'determiner' and 'complementiser' — and argues that neither of these categories is needed; and if this conclusion is correct, there is even le...

Entwining Structures in Monoidal Categories

Interpreting entwining structures as special instances of J. Beck’s distributive law, the concept of entwining module can be generalized for the setting of arbitrary monoidal category. In this paper, we use the distributive law formalism to extend in this setting basic properties of entwining modules.