Year: 2022
Type: article
Abstract: We prove that for each locally $$\alpha $$ α -presentable category $${\mathcal {K}}$$ K there exists a regular cardinal $$\gamma $$ γ such that any $$\alpha $$ α -accessible functor out of $${\mathcal {K}}$$ K (into another locally $$\alpha $$ α -presentable category) is continuous if and only if it preserves $$\gamma $$ γ -small limits; as a consequence we obtain a new adjoint functor theorem specific to the $$\alpha $$ α -accessible functors out of $${\mathcal {K}}$$ K . Afterwards we generalize these results to the enriched setting and deduce, among other things, that a small $${\mathcal {V}}$$ V -category is accessible if and only if it is Cauchy complete.
Source: Applied Categorical Structures
Author: Giacomo Tendas
Institution: Macquarie University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,780
Funder: Macquarie University
OpenAlex ID: W3209782450