3 citations · 6 across the 3 of their papers we have counts for
11 papers
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,…
Reiterman's Theorem on Finite Algebras for a Monad
Jiri Adamek, Liang-Ting Chen, Stefan Milius +1
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman's theorem states that they precisely specify pseudovarieties, i.e.~cla…
Finitary Monads on the Category of Posets
Jiří Adámek, Chase Ford, Stefan Milius +1
Finitary monads on are characterized as the precisely the free-algebra monads of varieties of algebras. These are classes of ordered algebras specified by inequation…
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…
On Finitary Functors
Jiří Adámek, Stefan Milius, Lurdes Sousa +1
A simple criterion for a functor to be finitary is presented: we call finitely bounded if for all objects every finitely generated subobject of factorizes through the…