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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Coends of Higher Arity

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Author(s):
Loregian, Fosco [1] ; Santos, Theo de Oliveira [2]
Total Authors: 2
Affiliation:
[1] Tallinn Univ Technol, Inst Cybernet, Akad Tee 15-2, EE-12618 Tallinn - Estonia
[2] Univ Sdo Paulo, Inst Ciencias Matemat & Computacdo, Av Trab Sao Carlense 400, BR-13566590 Sao Carlos - Brazil
Total Affiliations: 2
Document type: Journal article
Source: APPLIED CATEGORICAL STRUCTURES; AUG 2021.
Web of Science Citations: 0
Abstract

We specialise a recently introduced notion of generalised dinaturality for functors T : (C-op)(p) x C-q -> D to the case where the domain (resp., codomain) is constant, obtaining notions of ends (resp., coends) of higher arity, dubbed herein (p, q)-ends (resp., (p, q)-coends). While higher arity co/ends are particular instances of `totally symmetrised' (ordinary) co/ends, they serve an important technical role in the study of a number of new categorical phenomena, which may be broadly classified as two new variants of category theory. The first of these, weighted category theory, consists of the study of weighted variants of the classical notions and construction found in ordinary category theory, besides that of a limit. This leads to a host of varied and rich notions, such as weighted Kan extensions, weighted adjunctions, and weighted ends. The second, diagonal category theory, proceeds in a different (albeit related) direction, in which one replaces universality with respect to natural transformations with universality with respect to dinatural transformations, mimicking the passage from limits to ends. In doing so, one again encounters a number of new interesting notions, among which one similarly finds diagonal Kan extensions, diagonal adjunctions, and diagonal ends. (AU)

FAPESP's process: 20/02861-7 - A bird's-eye view of category theory
Grantee:Théo de Oliveira Santos
Support type: Scholarships in Brazil - Scientific Initiation