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@article{2355403,
author = {Lack, Stephen and Tendas, Giacomo},
article_number = {2},
doi = {http://dx.doi.org/10.1016/j.jpaa.2023.107444},
keywords = {Enriched categories; Accessible and locally presentable categories; Sketches and generalizations},
language = {eng},
issn = {0022-4049},
journal = {Journal of Pure and Applied Algebra},
title = {Accessible categories with a class of limits},
url = {https://doi.org/10.1016/j.jpaa.2023.107444},
volume = {228},
year = {2024}
}
TY - JOUR
ID - 2355403
AU - Lack, Stephen - Tendas, Giacomo
PY - 2024
TI - Accessible categories with a class of limits
JF - Journal of Pure and Applied Algebra
VL - 228
IS - 2
SP - 1-43
EP - 1-43
PB - Elsevier B.V.
SN - 00224049
KW - Enriched categories
KW - Accessible and locally presentable categories
KW - Sketches and generalizations
UR - https://doi.org/10.1016/j.jpaa.2023.107444
N2 - In this paper we characterize those accessible V-categories that have limits of a specified class. We do this by introducing the notion of companion C for a class of weights Ψ, as a collection of special types of colimit diagrams that are compatible with Ψ. We then characterize the accessible V-categories with Ψ-limits as those accessibly embedded and C-virtually reflective in a presheaf V-category, and as the V-categories of C-models of sketches. This allows us to recover the standard theorems for locally presentable, locally multipresentable, and locally polypresentable categories as instances of the same general framework. In addition, our theorem covers the case of any weakly sound class Ψ, and provides a new perspective on the case of weakly locally presentable categories.
ER -
LACK, Stephen and Giacomo TENDAS. Accessible categories with a class of limits. \textit{Journal of Pure and Applied Algebra}. Elsevier B.V., 2024, vol.~228, No~2, p.~1-43. ISSN~0022-4049. Available from: https://dx.doi.org/10.1016/j.jpaa.2023.107444.
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