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Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms of the inverse limit of an inverse family of finite partitions; this is an elementary and intuitive presentation of a consequence of the profiniteness of Stone spaces. We then apply this construction to answer a question of Rosinger posed in arXiv:0709.0084v2 in the negative.
This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finettis representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad.
We denote by Conc(A) the semilattice of compact congruences of an algebra A. Given a variety V of algebras, we denote by Conc(V) the class of all semilattices isomorphic to Conc(A) for some A in V. Given varieties V1 and V2 varieties of algebras, the
A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to $G$-crosse
We discuss the relationship between (co)homology groups and categorical diagonalization. We consider the category of chain complexes in the category of finitely generated free modules on a commutative ring. For a fixed chain complex with zero maps as
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics of algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or invariance und