A characterization of locally -presentable categories
A characterization of varieties of inverse semigroups.
A duality between infinitary varieties and algebraic theories
A duality between -ary varieties and -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal , whenever -small products commute with -colimits in , then must be a -filtered category. We nevertheless introduce the concept of -sifted colimits so that morphisms between -ary varieties (defined to be -ary, regular right adjoints) are precisely the functors...
A duality relative to a limit doctrine.
A logic of injectivity.
A note on algebraic categories
A note on categories enriched in quantaloids and modal and temporal logic
À propos de «Toposes, triples and theories» de messieurs M. Barr et C. Wells
A remark on topological spaces, grids, and topological systems
A theory of enriched sketches.
Algebraic localizations and elementary toposes
Algebraic models of intuitionistic theories of sets and classes.
Algebraic objects over a small category [Book]
Algebraic theories and varieties of functor algebras
Algèbres non déterministiques et -catégories
Algébricité, monadicité, esquissabilité et non-algébricité
An algebraic description of locally multipresentable categories.
Aspects of categorical algebra in initialstructure categories
Birkhoff's Covariety Theorem without limitations
J. Rutten proved, for accessible endofunctors of Set, the dual Birkhoff’s Variety Theorem: a collection of -coalgebras is presentable by coequations ( subobjects of cofree coalgebras) iff it is closed under quotients, subcoalgebras, and coproducts. This result is now proved to hold for all endofunctors of Set provided that coequations are generalized to mean subchains of the cofree-coalgebra chain. For the concept of coequation introduced by H. Porst and the author, which is a subobject of...
Birkhoff's variety theorem with and without free algebras.