Monads and theories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00113518" target="_blank" >RIV/00216224:14310/19:00113518 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0001870819302580" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0001870819302580</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2019.05.016" target="_blank" >10.1016/j.aim.2019.05.016</a>
Alternative languages
Result language
angličtina
Original language name
Monads and theories
Original language description
Given a locally presentable enriched category epsilon together with a small dense full subcategory A of arities, we study the relationship between monads on and identity-on-objects functors out of A, which we call A-pretheories. We show that the natural constructions relating these two kinds of structure form an adjoint pair. The fixpoints of the adjunction are characterised on the one side as the A-nervous monads-those for which the conclusions of Weber's nerve theorem hold-and on the other, as the A-theories which we introduce here. The resulting equivalence between A-nervous monads and A-theories is best possible in a precise sense, and extends almost all previously known monad-theory correspondences. It also establishes some completely new correspondences, including one which captures the globular theories defining Grothendieck weak omega-groupoids. Besides establishing our general correspondence and illustrating its reach, we study good properties of A-nervous monads and A-theories that allow us to recognise and construct them with ease. We also compare them with the monads with arities and theories with arities introduced and studied by Berger, Mellies and Weber.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
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Volume of the periodical
351
Issue of the periodical within the volume
JUL 31 2019
Country of publishing house
US - UNITED STATES
Number of pages
48
Pages from-to
1024-1071
UT code for WoS article
000475548900028
EID of the result in the Scopus database
2-s2.0-85066289226