Matches in SemOpenAlex for { <https://semopenalex.org/work/W2991863265> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2991863265 abstract "For functors $L:Ato B$ and $R:Bto A$ between any categories $A$ and $B$, a {em pairing} is defined by maps, natural in $Ain A$ and $Bin B$, $$xymatrix{Mor_B (L(A),B) ar@ [r]^{alpha} & Mor_A (A,R(B))ar@ [l]^{beta}}.$$ $(L,R)$ is an {em adjoint pair} provided $alpha$ (or $beta$) is a bijection. In this case the composition $RL$ defines a monad on the category $A$, $LR$ defines a comonad on the category $B$, and there is a well-known correspondence between monads (or comonads) and adjoint pairs of functors. For various applications it was observed that the conditions for a unit of a monad was too restrictive and weakening it still allowed for a useful generalised notion of a monad. This led to the introduction of {em weak monads} and {em weak comonads} and the definitions needed were made without referring to this kind of adjunction. The motivation for the present paper is to show that these notions can be naturally derived from pairings of functors $(L,R,alpha,beta)$ with $alpha = alphadcirc betadcirc alpha$ and $beta = beta dcircalphadcircbeta$. Following closely the constructions known for monads (and unital modules) and comonads (and counital comodules), we show that any weak (co)monad on $A$ gives rise to a regular pairing between $A$ and the category of {em compatible (co)modules}." @default.
- W2991863265 created "2019-12-13" @default.
- W2991863265 creator A5064059395 @default.
- W2991863265 date "2011-01-06" @default.
- W2991863265 modified "2023-09-27" @default.
- W2991863265 title "Adjunction contexts and regular quasi-monads" @default.
- W2991863265 cites W1527324030 @default.
- W2991863265 cites W1709148114 @default.
- W2991863265 cites W1963727942 @default.
- W2991863265 cites W2011673663 @default.
- W2991863265 cites W2025143663 @default.
- W2991863265 cites W2034853716 @default.
- W2991863265 cites W2047862786 @default.
- W2991863265 cites W2077661136 @default.
- W2991863265 cites W2112435916 @default.
- W2991863265 cites W2329010518 @default.
- W2991863265 cites W2944306120 @default.
- W2991863265 cites W3133287349 @default.
- W2991863265 hasPublicationYear "2011" @default.
- W2991863265 type Work @default.
- W2991863265 sameAs 2991863265 @default.
- W2991863265 citedByCount "1" @default.
- W2991863265 countsByYear W29918632652012 @default.
- W2991863265 crossrefType "posted-content" @default.
- W2991863265 hasAuthorship W2991863265A5064059395 @default.
- W2991863265 hasConcept C105795698 @default.
- W2991863265 hasConcept C114614502 @default.
- W2991863265 hasConcept C121332964 @default.
- W2991863265 hasConcept C136119220 @default.
- W2991863265 hasConcept C14103023 @default.
- W2991863265 hasConcept C156772000 @default.
- W2991863265 hasConcept C171606756 @default.
- W2991863265 hasConcept C199360897 @default.
- W2991863265 hasConcept C202444582 @default.
- W2991863265 hasConcept C24424167 @default.
- W2991863265 hasConcept C2776174256 @default.
- W2991863265 hasConcept C2780580338 @default.
- W2991863265 hasConcept C33923547 @default.
- W2991863265 hasConcept C33959348 @default.
- W2991863265 hasConcept C41008148 @default.
- W2991863265 hasConcept C49453240 @default.
- W2991863265 hasConcept C54101563 @default.
- W2991863265 hasConcept C62520636 @default.
- W2991863265 hasConcept C64943373 @default.
- W2991863265 hasConceptScore W2991863265C105795698 @default.
- W2991863265 hasConceptScore W2991863265C114614502 @default.
- W2991863265 hasConceptScore W2991863265C121332964 @default.
- W2991863265 hasConceptScore W2991863265C136119220 @default.
- W2991863265 hasConceptScore W2991863265C14103023 @default.
- W2991863265 hasConceptScore W2991863265C156772000 @default.
- W2991863265 hasConceptScore W2991863265C171606756 @default.
- W2991863265 hasConceptScore W2991863265C199360897 @default.
- W2991863265 hasConceptScore W2991863265C202444582 @default.
- W2991863265 hasConceptScore W2991863265C24424167 @default.
- W2991863265 hasConceptScore W2991863265C2776174256 @default.
- W2991863265 hasConceptScore W2991863265C2780580338 @default.
- W2991863265 hasConceptScore W2991863265C33923547 @default.
- W2991863265 hasConceptScore W2991863265C33959348 @default.
- W2991863265 hasConceptScore W2991863265C41008148 @default.
- W2991863265 hasConceptScore W2991863265C49453240 @default.
- W2991863265 hasConceptScore W2991863265C54101563 @default.
- W2991863265 hasConceptScore W2991863265C62520636 @default.
- W2991863265 hasConceptScore W2991863265C64943373 @default.
- W2991863265 hasLocation W29918632651 @default.
- W2991863265 hasOpenAccess W2991863265 @default.
- W2991863265 hasPrimaryLocation W29918632651 @default.
- W2991863265 hasRelatedWork W1002042951 @default.
- W2991863265 hasRelatedWork W1553024573 @default.
- W2991863265 hasRelatedWork W1572021354 @default.
- W2991863265 hasRelatedWork W1813933622 @default.
- W2991863265 hasRelatedWork W1969245692 @default.
- W2991863265 hasRelatedWork W1976826114 @default.
- W2991863265 hasRelatedWork W1994430959 @default.
- W2991863265 hasRelatedWork W2009139565 @default.
- W2991863265 hasRelatedWork W2017778827 @default.
- W2991863265 hasRelatedWork W2034853716 @default.
- W2991863265 hasRelatedWork W2059425538 @default.
- W2991863265 hasRelatedWork W2148034910 @default.
- W2991863265 hasRelatedWork W2183938998 @default.
- W2991863265 hasRelatedWork W2497414066 @default.
- W2991863265 hasRelatedWork W2773225929 @default.
- W2991863265 hasRelatedWork W2952692115 @default.
- W2991863265 hasRelatedWork W2955614155 @default.
- W2991863265 hasRelatedWork W2962963437 @default.
- W2991863265 hasRelatedWork W3099931493 @default.
- W2991863265 hasRelatedWork W2183400106 @default.
- W2991863265 isParatext "false" @default.
- W2991863265 isRetracted "false" @default.
- W2991863265 magId "2991863265" @default.
- W2991863265 workType "article" @default.