3 citations · 6 across the 3 of their papers we have counts for
5 papers · 1 filter
Algebraic cocompleteness and finitary functors
Jiri Adamek
A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and,…
On Well-Founded and Recursive Coalgebras
Jiří Adámek, Stefan Milius, Lawrence S. Moss
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive…
On free completely iterative algebras
Jiri Adamek
For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative co…
Syntactic Monoids in a Category
Jiri Adamek, Stefan Milius, Henning Urbat
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category D. This allows for a uniform treatment of several notions of syntactic algebr…
On coalgebra based on classes
J. Adamek, S. Milius, J. Velebil
Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endof…