Related papers: Canonical Selection of Colimits
Colimits are a fundamental construction in category theory. They provide a way to construct new objects by gluing together existing objects that are related in some way. We introduce a complementary notion of anticolimits, which provide a…
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we…
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…
A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a…
We show that there are infinitely many distinct closed classes of colimits (in the sense of the Galois connection induced by commutation of limits and colimits in Set) which are intermediate between the class of pseudo-filtered colimits and…
We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about \'etale…
The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriated framework to specify and integrate learning processes, data transformation processes and…
We show how finite limits and colimits can be calculated compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages.
Lexical selection in Machine Translation consists of several related components. Two that have received a lot of attention are lexical mapping from an underlying concept or lexical item, and choosing the correct subcategorization frame…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Combinatorial optimization augmented machine learning (COAML) has recently emerged as a powerful paradigm for integrating predictive models with combinatorial decision-making. By embedding combinatorial optimization oracles into learning…
Is there a characteristic of coordination languages that makes them qualitatively different from general programming languages and deserves special academic attention? This report proposes a nuanced answer in three parts. The first part…
In this thesis weighted colimits in 2-categories equipped with promorphisms are studied. Such colimits include most universal constructions with counits, like ordinary colimits in categories, weighted colimits in enriched categories, and…
In this article we present a detailed study of the existing constructions of colilimits in the category of symmetrical operations. In addition, some examples of operads obtained from colimits of other operads are presented.
Chemical language models (CLMs) are increasingly used for molecular design and property prediction. Because these models learn from textual encodings of molecules, differences in how such encodings are generated may affect their behavior.…
Higher Homotopy van Kampen Theorems allow the computation as colimits of certain homotopical invariants of glued spaces. One corollary is to describe homotopical excision in critical dimensions in terms of induced modules and crossed…
For a strongly connected category $\mathcal C$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of ${\sf lim} : \mathrm{Ab}^{\mathcal C}\to…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Our study demonstrates the effective use of Large Language Models (LLMs) for automating the classification of complex datasets. We specifically target proposals of Decentralized Autonomous Organizations (DAOs), as the clas-sification of…
We show that the category of comodules over a coassociative coalgebra in a complete, cocomplete and well-powered category has limits and colimits under additional assumptions.