The Heteromorphic Approach to Adjunctions: Theory and History
MathematicsMallios and Zafiris emphasize that adjoint functors, or adjunctions, are not only “ubiquitous” in category theory but also characterize the naturality of their approach to physical geometry.
David Ellerman, Ellerman David
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Isbell Adjunctions and Kan Adjunctions via Quantale-Enriched Two-Variable Adjunctions [PDF]
Applied Categorical Structures, 2021 It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions constructed from suitable associated two-variable adjunctions.
Lili Shen
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Spherical Monadic Adjunctions of Stable Infinity Categories
International Mathematics Research Notices, 2022 This paper concerns spherical adjunctions of stable $\infty$-categories and their relation to monadic adjunctions. We begin with a proof of the 2/4 property of spherical adjunctions in the setting of stable $\infty$-categories.
Christ, Merlin
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Where Do Adjunctions Come From? Chimera Morphisms and Adjoint Functors in Category Theory [PDF]
FoundationsCategory theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints come from”. The
David Ellerman
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Journal of Pure and Applied Algebra, 1988 The concept of a local adjunction between bicategories A and B focuses on a family of adjunctionsB(FA, B)⇆A(A, GB) between hom-categories; hence the name local adjunction. When bicategories of spans, or (bi-)modules for some monoidal category are created,
Jay, C.Barry
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Comparative analysis of fungal and bacterial composition in natural wines and their closest pesticide-treated counterparts [PDF]
Scientific ReportsFermentation produces diverse consumables like bread, wine, beer, and cheese, with fungi playing a key role. This study sequenced fungal and bacteria DNA from 46 commercial wines, paired by vineyard proximity, harvest time, and grape variety. One in each
Robin Mesnage +2 more
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Complementary and integrative medicine - Resolving situations of reduced remuneration for additional work under the SwissDRG system [PDF]
HeliyonAim of the study: Complementary and integrative medicine (CIM) has been increasingly recognized as offering promising treatment adjunctions in various clinical settings, even amongst patients with serious, chronic, or recurrent illness.
Fabian Grass +4 more
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Categorial compositionality II: universal constructions and a general theory of (quasi-)systematicity in human cognition. [PDF]
PLoS Computational Biology, 2011 A complete theory of cognitive architecture (i.e., the basic processes and modes of composition that together constitute cognitive behaviour) must explain the systematicity property--why our cognitive capacities are organized into particular groups of ...
Steven Phillips, William H Wilson
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Adjunctions on the lattices of partitions and of partial partitions
Applicable Algebra in Engineering, Communications and Computing, 2010 International audienceThe complete lattice Π(E) of partitions of a space E has been extended into Π * (E), the one of partial partitions of E (where the space covering axiom is removed).
Christian Ronse, Ronse Christian
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