Formal coalgebras and applications

Localization in Coalgebras. Applications to Finiteness Conditions

Let k be a field. Given two finite-dimensional right comodules N andM over a k–coalgebra C, the k–vector spaces ExtC(N,M) need not to be finite-dimensional. This is due to the fact that the injective right comodules appearing in the minimal injective resolution of M need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules a...

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

Formal islands: foundations and applications

?Logic and Formal Ontology: Is the Final Formal Ontology Possible

Musa Akrami AbstractMany philosophers and logicians have contemplated the relationship between ontology and logic. The author of this paper, working within a Bolzanoan-Husserlian tradition of studying both ontology and logic, considers ontology as the science of the most general features of beings and the most general relations among them. He considers logic as the science concernin...

Formal islands: foundations and applications

Formal islands: foundations and applications IN COLLABORATION WITH: Laboratoire lorrain de recherche en informatique et ses applications (LORIA)