Bigger diagrams make visible more automorphisms: more precisely, bigger diagrams with the same limit make visible more automorphisms of the same object. In the case of the 2-solenoid, this means that we will find a copy of the 2-adic rational numbers [1] Q2 acting on the 2-solenoid, rather than merely the 2-adic integers Z2. This is a big change in the sense that Q2 is non-compact, while Z2 is ...

Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis? We propose to use the language of category theory, in particular diagrams and their colimits, for answering this question. We outline a general approach for representing combinations of logical theories, or ontologies, through interfaces of various kinds, based on diagrams and ...

We consider the equivalence of Lawvere theories and finitary monads on Set from the perspective of Endf (Set)-enriched category theory, where Endf (Set) is the category of finitary endofunctors of Set. We identify finitary monads with one-object Endf (Set)-categories, and ordinary categories admitting finite powers (i.e., n-fold products of each object with itself) with Endf (Set)-categories ad...

We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced by an endomorphism of the diagram, then its trace can be calculated as a linear combination of traces on the objects in the diagram. The formal nature of th...

We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors T. C —» D between small categories with finite limits for which the functor /*: LEX(D,Set) —> LEX...

Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our first goal is to explain both and show their equivalence. Our second goal is to generalize this result to enriched categories and homotopy weighted limits, s...

It is possible to translate a modified version of K. Worytkiewicz’s combinatorial semantics of CCS (Milner’s Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled flows using a geometric realization functor. It turns out that a satisfactory semantics in terms of flows requires to work directly in their homotopy category ...

We study properties of the quantale spectrum MaxA of an arbitrary unital C*-algebra A. In particular we show that the spatialization of MaxA with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when A is commutative. We study under general conditions functors with this property, in addition requiring that colimits be preserved, and we conclu...