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Cubical Sets and Trace Monoid Actions [PDF]

open access: yesThe Scientific World Journal, 2013
This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets.
Ahmet A. Husainov
doaj   +2 more sources

Adjoint functors and triples [PDF]

open access: bronze, 1965
A riple F (F, ,) in ctegory a consists of functor F a nd morphisms la F, F F stisfying some identities (see 2, (T.1)-(T.3)) nlogous to those stisfied in monoid. Cotriples re defined dually.
Samuel Eilenberg, John C. Moore
openalex   +2 more sources

Adjoints and emergence: applications of a new theory of adjoint functors [PDF]

open access: hybrid, 2007
Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality ...
David Ellerman
openalex   +2 more sources

Adjoint and Frobenius Pairs of Functors, Equivalences, and the Picard Group for Corings [PDF]

open access: greenarXiv, 2007
We study adjoint and Frobenius pairs of functors, equivalences, and the Picard group for corings.
Mohssin Zarouali-Darkaoui
openalex   +3 more sources

On Adjoint and Brain Functors [PDF]

open access: green, 2015
There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory.
David Ellerman
openalex   +3 more sources

Planar diagrammatics of self-adjoint functors and recognizable tree series [PDF]

open access: yesPure and Applied Mathematics Quarterly, 2021
A pair of biadjoint functors between two categories produces a collection of elements in the centers of these categories, one for each isotopy class of nested circles in the plane.
M. Khovanov, Robert Laugwitz
semanticscholar   +1 more source

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