Matches in SemOpenAlex for { <https://semopenalex.org/work/W2146563885> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2146563885 abstract "Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We also expand on an undeservedly ignored theorem of Kennison and Gildenhuys: that the codensity monad of the inclusion of (finite sets) into (sets) is the ultrafilter monad. This result is analogous to the correspondence between measures and integrals. So, for example, we can speak of integration against an ultrafilter. Using this language, we show that the codensity monad of the inclusion of (finite-dimensional vector spaces) into (vector spaces) is double dualization. From this it follows that compact Hausdorff spaces have a linear analogue: linearly compact vector spaces. Finally, we show that ultraproducts are categorically inevitable: the codensity monad of the inclusion of (finite families of sets) into (families of sets) is the ultraproduct monad." @default.
- W2146563885 created "2016-06-24" @default.
- W2146563885 creator A5047971691 @default.
- W2146563885 date "2012-09-17" @default.
- W2146563885 modified "2023-09-27" @default.
- W2146563885 title "Codensity and the ultrafilter monad" @default.
- W2146563885 cites W1036696047 @default.
- W2146563885 cites W147115492 @default.
- W2146563885 cites W1500433795 @default.
- W2146563885 cites W1510067240 @default.
- W2146563885 cites W1548944036 @default.
- W2146563885 cites W1567997956 @default.
- W2146563885 cites W1971195030 @default.
- W2146563885 cites W2006735442 @default.
- W2146563885 cites W2038835699 @default.
- W2146563885 cites W2047862786 @default.
- W2146563885 cites W2055843813 @default.
- W2146563885 cites W2083259718 @default.
- W2146563885 cites W2120713972 @default.
- W2146563885 cites W2143682387 @default.
- W2146563885 cites W2529887420 @default.
- W2146563885 cites W2732021604 @default.
- W2146563885 cites W2799061192 @default.
- W2146563885 cites W3039671159 @default.
- W2146563885 cites W3141871949 @default.
- W2146563885 cites W342302233 @default.
- W2146563885 cites W565628694 @default.
- W2146563885 cites W594070437 @default.
- W2146563885 cites W69808434 @default.
- W2146563885 hasPublicationYear "2012" @default.
- W2146563885 type Work @default.
- W2146563885 sameAs 2146563885 @default.
- W2146563885 citedByCount "1" @default.
- W2146563885 countsByYear W21465638852016 @default.
- W2146563885 crossrefType "posted-content" @default.
- W2146563885 hasAuthorship W2146563885A5047971691 @default.
- W2146563885 hasConcept C118615104 @default.
- W2146563885 hasConcept C136119220 @default.
- W2146563885 hasConcept C156772000 @default.
- W2146563885 hasConcept C167930466 @default.
- W2146563885 hasConcept C191399826 @default.
- W2146563885 hasConcept C202444582 @default.
- W2146563885 hasConcept C33923547 @default.
- W2146563885 hasConcept C33959348 @default.
- W2146563885 hasConcept C87598191 @default.
- W2146563885 hasConceptScore W2146563885C118615104 @default.
- W2146563885 hasConceptScore W2146563885C136119220 @default.
- W2146563885 hasConceptScore W2146563885C156772000 @default.
- W2146563885 hasConceptScore W2146563885C167930466 @default.
- W2146563885 hasConceptScore W2146563885C191399826 @default.
- W2146563885 hasConceptScore W2146563885C202444582 @default.
- W2146563885 hasConceptScore W2146563885C33923547 @default.
- W2146563885 hasConceptScore W2146563885C33959348 @default.
- W2146563885 hasConceptScore W2146563885C87598191 @default.
- W2146563885 hasLocation W21465638851 @default.
- W2146563885 hasOpenAccess W2146563885 @default.
- W2146563885 hasPrimaryLocation W21465638851 @default.
- W2146563885 hasRelatedWork W1881093659 @default.
- W2146563885 hasRelatedWork W1887024729 @default.
- W2146563885 hasRelatedWork W1972405505 @default.
- W2146563885 hasRelatedWork W2009139565 @default.
- W2146563885 hasRelatedWork W2151448345 @default.
- W2146563885 hasRelatedWork W2164268874 @default.
- W2146563885 hasRelatedWork W2186456475 @default.
- W2146563885 hasRelatedWork W2604066929 @default.
- W2146563885 hasRelatedWork W2769923424 @default.
- W2146563885 hasRelatedWork W2805631771 @default.
- W2146563885 hasRelatedWork W2897197486 @default.
- W2146563885 hasRelatedWork W2942282180 @default.
- W2146563885 hasRelatedWork W2949373865 @default.
- W2146563885 hasRelatedWork W2962755707 @default.
- W2146563885 hasRelatedWork W2962963437 @default.
- W2146563885 hasRelatedWork W2970491490 @default.
- W2146563885 hasRelatedWork W3098518392 @default.
- W2146563885 hasRelatedWork W3105836415 @default.
- W2146563885 hasRelatedWork W3121177248 @default.
- W2146563885 hasRelatedWork W1970598198 @default.
- W2146563885 isParatext "false" @default.
- W2146563885 isRetracted "false" @default.
- W2146563885 magId "2146563885" @default.
- W2146563885 workType "article" @default.