Results 21 to 30 of about 100,519 (222)
Unifilar Machines and the Adjoint Structure of Bayesian Filtering [PDF]
ACT, 2023 We elucidate the mathematical structure of Bayesian filtering, and Bayesian inference more broadly, by applying recent work on category theoretical probability, specifically the concept of a strongly representable Markov category. We show that filtering,
Nathaniel Virgo
semanticscholar +1 more source
The core of adjoint functors [PDF]
Theory and Applications of Categories, 2012 There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, which we then apply to internal categories. Finally, we describe a doctrinal setting.
Ross Street
openalex +4 more sources
Crossed modules bifibred over k-Algebras
Cumhuriyet Science Journal, 2021 In this paper we examine on a pair of adjoint functors (ϕ^* ,ϕ_*)for a subcategory of the category of crossed modules over commutative algebras where ϕ_*: XMod/P → XMod/Q, induced, and ϕ^*:XMod/Q → XMod/P, pullback (co-induced), which enables us to move
Özgün Gürmen Alansal +1 more
doaj +1 more source
Adjoint functors in graph theory [PDF]
, 2013 We survey some uses of adjoint functors in graph theory pertaining to colourings, complexity reductions, multiplicativity, circular colourings and tree duality. The exposition of these applications through adjoint functors unifies the presentation to some extent, and also raises interesting questions.
Jan Foniok, Claude Tardif
openalex +3 more sources
The left adjoint of derived parabolic induction [PDF]
Mathematische Zeitschrift, 2022 We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod p representations of a p -adic reductive group, admits a left adjoint $$\textrm{L}(U,-)$$ L ( U , - ) .
Claudius Heyer
semanticscholar +1 more source
Lagrangian cobordism functor in microlocal sheaf theory I [PDF]
Journal of Topology, 2021 Let Λ±$\Lambda _\pm$ be Legendrian submanifolds in the cosphere bundle T∗,∞M$T^{*,\infty }M$ . Given a Lagrangian cobordism L$L$ of Legendrians from Λ−$\Lambda _-$ to Λ+$\Lambda _+$ , we construct a functor ΦL*:ShΛ+c(M)→ShΛ−c(M)⊗C−*(Ω*Λ−)C−*(Ω*L ...
Wenyuan Li
semanticscholar +1 more source
Free Applicative Functors [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 Applicative functors are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell.
Paolo Capriotti, Ambrus Kaposi
doaj +1 more source
A note on a free group. The decomposition of a free group functor through the category of heaps [PDF]
International Electronic Journal of Algebra, 2021 This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it to describe a
Bernard Rybolowicz
semanticscholar +1 more source
Planar diagrammatics of self-adjoint functors and recognizable tree series [PDF]
Pure 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