Algebraically cocomplete categories
 
 
Description:  Dualizing the concept introduced by Freyd in 1990, a category is called algebraically cocomplete if every endofunctor has a terminal coalgebra. Among cocomplete categories these are just preordered classes. However, assuming the generalized continuum hypothesis (GCH), we present nice examples: the category Set_k of sets of power at most k is algebraically cocomplete for all uncountable regular cardinals k. (In contrast, the category of countable sets is algebraically complete, but not cocomplete.) Also the category Vec_k of vector spaces of dimension a most k is algebraically cocomplete and, given a finite group G, so is the category G-Set_k of G-sets of power at most k.

The assumption of GCH cannot be simply omitted: we prove that the continuum hypothesis is *equivalent* to the statement that the category of sets of power at most aleph_1 is algebraically cocomplete.
Date:  2021-04-13
Start Time:   15:00
Speaker:  Jiri Adámek (Technische Universität Braunschweig, Germany)
Institution:  Technische Universität Braunschweig
Place:  Zoom
Research Groups: -Algebra, Logic and Topology
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Science and Technology Foundation
Financiado total ou parcialmente pela FCT, Fundação para a Ciência e a Tecnologia, I.P., sob o Financiamento de:
UID/00324/2025 Projeto Estratégico com a referência DOI https://doi.org/10.54499/UID/00324/2025.
https://doi.org/10.54499/UID/PRR/00324/2025     UID/PRR/00324/2025   https://doi.org/10.54499/UID/PRR2/00324/2025   UID/PRR2/00324/2025
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