Related papers: When a matrix condition implies the Mal'tsev prope…
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
The main aim of this note is to show that, in the regular context, every matrix property in the sense of Z. Janelidze either implies the Mal'tsev property, or is implied by the majority property. When the regular category is arithmetical,…
Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev condition. We present a new, relatively simple Maltsev…
A classification theorem for three different sorts of Mal'tsev categories is proven. The theorem provides a classification for Mal'tsev category, naturally Malt'sev category, and weakly Mal'tsev category in terms of classifying classes of…
The notion of a weakly Mal'tsev category, as it was introduced in 2008 by the third author, is a generalization of the classical notion of a Mal'tsev category. It is well-known that a variety of universal algebras is a Mal'tsev category if…
In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a fixed (strong) Maltsev condition $\Sigma$. Our goal in this paper is to show that $\Sigma$-testing can be accomplished…
It is known that any finite idempotent algebra that satisfies a nontrivial Maltsev condition must satisfy the linear one-equality Maltsev condition (a variant of the term discovered by M. Siggers and refined by K. Kearnes, P. Markovi\'c,…
This paper provides a short introduction to the notion of regular category and its use in categorical algebra. We first prove some of its basic properties, and consider some fundamental algebraic examples. We then analyse the algebraic…
We explore a hierarchy of notions in categorical algebra: Mal'tsev categories (where every reflexive relation is symmetric); naturally Mal'tsev categories (where every reflexive graph underlies a unique internal groupoid structure, also…
Mal'tsev categories turned out to be a central concept in categorical algebra. On one hand, the simplicity and the beauty of the notion is revealed through a lot of characterizations of different flavour. Depending on the context, one can…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
We extend a well-known theorem of Murski\v{\i} to the probability space of finite models of a system $\mathcal{M}$ of identities of a strong idempotent linear Maltsev condition. We characterize the models of $\mathcal{M}$ in a way that can…
The main result of this paper shows that if $\mathcal{M}$ is a consistent strong linear Maltsev condition which does not imply the existence of a cube term, then for any finite algebra $\mathbb{A}$ there exists a new finite algebra…
We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.
In this paper, we investigate the property (P) that finite products commute with arbitrary coequalizers in pointed categories. Examples of such categories include any regular unital or (pointed) majority category with coequalizers, as well…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent…