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Torsion in one-term distributive homology

Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra (2014)

Fundamenta Mathematicae

The one-term distributive homology was introduced in [Prz] as an atomic replacement of rack and quandle homology, which was first introduced and developed by Fenn-Rourke-Sanderson [FRS] and Carter-Kamada-Saito [CKS]. This homology was initially suspected to be torsion-free [Prz], but we show in this paper that the one-term homology of a finite spindle may have torsion. We carefully analyze spindles of block decomposition of type (n,1) and introduce various techniques to compute their homology precisely....

Totality of colimit closures

Reinhard Börger, Walter Tholen (1991)

Commentationes Mathematicae Universitatis Carolinae

Adámek, Herrlich, and Reiterman showed that a cocomplete category 𝒜 is cocomplete if there exists a small (full) subcategory ℬ such that every 𝒜 -object is a colimit of ℬ -objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions...

Totality of product completions

Jiří Adámek, Lurdes Sousa, Walter Tholen (2000)

Commentationes Mathematicae Universitatis Carolinae

Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category 𝒜 by asking the Yoneda embedding 𝒜 → [ 𝒜 o p , 𝒮 e t ] to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion Π 𝒜 of 𝒜 . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product...

Towards a logic of semiotic systems

Constantin Thiopoulos (1992)

Mathématiques et Sciences Humaines

The rationalistic denotational approach to semantics is not adequate for capturing the structural dimension of meaning, which is immanent in semiotic systems. The demand for a structural approach to semantics is intensified by a turn in Artificial Intelligence, introduced by Connectionism and Information Retrieval. This paper presents such a structural approach to semantics founded on the phenomenological and autopoietic paradigms and proposes a formalization with the help of category theory.

Tower extension of topological constructs

De Xue Zhang (2000)

Commentationes Mathematicae Universitatis Carolinae

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct 𝐂 ( L ) , called the tower extension of 𝐂 (indexed by L ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot...

Traced premonoidal categories

Nick Benton, Martin Hyland (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.

Traced Premonoidal Categories

Nick Benton, Martin Hyland (2010)

RAIRO - Theoretical Informatics and Applications

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in Cartesian categories.

Transfer of derived equivalences from subalgebras to endomorphism algebras II

Shengyong Pan, Jiahui Yu (2024)

Czechoslovak Mathematical Journal

We investigate derived equivalences between subalgebras of some Φ -Auslander-Yoneda algebras from a class of n -angles in weakly n -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by n -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to n -angle cases. Finally, we give an explicit example to illustrate our result.

Currently displaying 241 – 260 of 278