Grothendieck toposes are studied via the process of taking the associated Sl-enriched category of relations. It is shown that this process is adjoint to that of taking the topos of sheaves of an abstract category of relations. As a result, pullback and comma toposes are calculated in a new way. The calculations are used to give a new characterization of localic morphisms and to derive interpola...

Several methods for constructing left determined model structures are expounded. The starting point is Olschok’s work on locally presentable categories. We give sufficient conditions to obtain left determined model structures on a full reflective subcategory, on a full coreflective subcategory and on a comma category. An application is given by constructing a left determined model structure on ...

A category CoLog of distributive laws is introduced to unify different approaches to modal logic for coalgebras, based merely on the presence of a contravariant functor P that maps a state space to its collection of predicates. We show that categorical constructions, including colimits, limits, and compositions of distributive laws as a tensor product, in CoLog generalise and extend existing co...

For each recollement of triangulated categories, there is an epivalence between the middle category and comma associated with a triangle functor from on right to left. morphic enhancement $\mathcal {T}$ , are three explicit ideals enhancing category, whose corresponding factor categories all equivalent module over . Examples related inflation weighted projective lines discussed.

New varieties of comma-free codes CFC of length 3 on the 4-letter alphabet are defined and analysed: self-complementary comma-free codes (CCFC), C3 comma-free codes (C3CFC), C3 self-complementary comma-free codes (C3CCFC), selfcomplementary maximal comma-free codes (CMCFC), C3 maximal comma-free codes (C3MCFC) and C3 self-complementary maximal comma-free codes (C3CMCFC). New properties with wor...

In this paper, we introduce the notion of k-comma codes a proper generalization of the notion of comma-free codes. For a given positive integer k, a k-comma code is a set L over an alphabet Σ with the property that LΣL ∩ ΣLΣ = ∅. Informally, in a k-comma code, no codeword can be a subword of the catenation of two other codewords separated by a “comma” of length k. A k-comma code is indeed a cod...

Spans are pairs of arrows with a common domain. Despite their symmetry, spans are frequently viewed as oriented transitions from one of the codomains to the other codomain. The transition along an oriented span might be thought of as transitioning backwards along the first arrow (sometimes called ‘leftwards’) and then, having reached the common domain, forwards along the second arrow (sometimes...

The comma is the most common form of punctuation. As such, it may have the greatest effect on the syntactic analysis of a sentence. As an isolate language, Chinese sentences have fewer cues for parsing. The clues for segmentation of a long Chinese sentence are even fewer. However, the average frequency of comma usage in Chinese is higher than other languages. The comma plays an important role i...

This research exploits the view of constraint programming as computation in a logical system, namely constraint logic. The basic ingredients of constraint logic are: constraint models for the semantics (they form a comma-category over a fixed model of “built-ins”), generalized polynomials in the rôle of basic syntactic ingredient, and a constraint satisfaction relation between semantics and syn...

This paper proposes a method for automatically inserting commas into Japanese texts. In Japanese sentences, commas play an important role in explicitly separating the constituents, such as words and phrases, of a sentence. The method can be used as an elemental technology for natural language generation such as speech recognition and machine translation, or in writing-support tools for non-nati...