Factorization systems and double categories

ŠTĚPÁN, Miloslav. Factorization systems and double categories. Theory and Applications of Categories. Mount Allison University, 2024, vol. 41, No 18, p. 551-592, 43 pp. ISSN 1201-561X.

Basic information

• Original name: Factorization systems and double categories
• Authors: ŠTĚPÁN, Miloslav (203 Czech Republic, guarantor, belonging to the institution).
• Edition: Theory and Applications of Categories, Mount Allison University, 2024, 1201-561X.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Canada
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.500 in 2022
• Organization unit: Faculty of Science
• UT WoS: 001231984000001
• Keywords in English: factorization system; double category; lax morphism
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

We show that factorization systems, both strict and orthogonal, can be equivalently described as double categories satisfying certain properties. This provides conceptual reasons for why the category of sets and partial maps or the category of small categories and cofunctors admit orthogonal factorization systems. The theory also gives an explicit description of various lax morphism classifiers and explains why they admit strict factorization systems.

Links

• EF19_073/0016943, research and development project: Name: Interní grantová agentura Masarykovy univerzity
• GA22-02964S, research and development project: Name: Obohacené kategorie a jejich aplikace (Acronym: ECATA)

Investor: Czech Science Foundation