45 citations · 118 across the 19 of their papers we have counts for
27 papers
Smallness in Topology
Jiri Adamek, Miroslav Husek, Jiri Rosicky +1
Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notio…
Varieties of ordered algebras as categories
Jiří Adámek, Jiří Rosický
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent…
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 the Behaviour of Coalgebras with Side Effects and Algebras with Effectful Iteration
Stefan Milius, Jiří Adámek, Henning Urbat
For every finitary monad on sets and every endofunctor on the category of -algebras we introduce the concept of an ffg-Elgot algebra for , that is, an algebra admitti…
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…
Algebraic cocompleteness and finitary functors
Jiří Adámek
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 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…
Colimit-Dense Subcategories
J. Adámek, A. Brooke-Taylor, T. Campion +2
Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vop{ě}nka's Principle, we prov…
A Categorical Approach to Syntactic Monoids
Jiří Adamek, Stefan Milius, Henning Urbat
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category . This allows for a uniform treatment of several notions of synta…
On Corecursive Algebras for Functors Preserving Coproducts
Jiří Adámek, Stefan Milius
For an endofunctor on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on as the coproduct of the final coalgebra for …
Eilenberg Theorems for Free
Henning Urbat, Jiří Adámek, Liang-Ting Chen +1
Eilenberg-type correspondences, relating varieties of languages (e.g. of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebra…
Profinite Monads, Profinite Equations, and Reiterman's Theorem
Liang-Ting Chen, Jiri Adamek, 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…
On reflective subcategories of locally presentable categories
Jiri Adamek, Jiri Rosicky
Are all subcategories of locally finitely presentable categories that are closed under limits and -filtered colimits also locally presentable? For full subcategories the answer…
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…
Varieties of Languages in a Category
Jiri Adamek, Stefan Milius, Robert Myers +1
Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a bijective correspondence between varieties of languages and pseudovarieties of monoids. In th…
Generalized Eilenberg Theorem I: Local Varieties of Languages
Jiri Adamek, Stefan Milius, Robert Myers +1
We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg's theorem. This theorem states th…
Colimits of Monads
Jiří Adámek
The category of all monads over many-sorted sets (and over other "set-like" categories) is proved to have coequalizers and strong cointersections. And a general diagram has a colim…
Corecursive Algebras, Corecursive Monads and Bloom Monads
Jiří Adámek, Mahdie Haddadi, Stefan Milius
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproduc…
Kan injectivity in order-enriched categories
Jiri Adamek, Lurdes Sousa, Jiri Velebil
Continuous lattices were characterised by Martin Escardo as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general ca…
Well-Pointed Coalgebras
Jiří Adámek, Stefan Milius, Lawrence S Moss +1
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalg…
Semantics of Higher-Order Recursion Schemes
Jiri Adamek, Stefan Milius, Jiri Velebil
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted…