Results 171 to 180 of about 37,460 (208)

Adjunctions and Adjoint Functor Theorems

2021
In this section, we will discuss adjunctions between ∞-categories. We will define them in the language of fibrations and show that they may equivalently be described by choosing a binatural transformation of bivariant mapping-space functors. We will give several sufficient criteria for a fixed functor \(f \colon \mathscr {C} \to \mathscr {D}\) to admit
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Equivalences Induced by Adjoint Functors

Communications in Algebra, 2003
Abstract Let 𝒜 and ℬ be two Grothendieck categories, R : 𝒜 → ℬ, L : ℬ → 𝒜 a pair of adjoint functors, S ∈ ℬ a generator, and U = L(S). U defines a hereditary torsion class in 𝒜, which is carried by L, under suitable hypotheses, into a hereditary torsion class in ℬ. We investigate necessary and sufficient conditions which
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ORDER EXTENSIONS AS ADJOINT FUNCTORS

Quaestiones Mathematicae, 1986
Abstract A standard extension (resp. standard completion) is a function Z assigning to each poset P a (closure) system ZP of subsets such that x ⋚ y iff x belongs to every Z e ZP with y e Z. A poset P is Z -complete if each Z e 2P has a join in P. A map f: P → P′ is Z—continuous if f−1 [Z′] e ZP for all Z′ e ZP′, and a Z—morphism if, in addition, for ...
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Adjoint Functors and Representation Dimensions

Acta Mathematica Sinica, English Series, 2006
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
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RESTRICTED ADJOINTS AND TOPOLOGICAL FUNCTORS

Quaestiones Mathematicae, 1983
Abstract The idea of adjoint functors or adjoint situation is one of the most important concepts in category theory. However, many examples are known which deviate from adjoint situations in one respect or another. These gave rise to various generalizations of adjoint situations (e.g. see R. Borger and w. Tholen [l], Y. Diers [2], and F.
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Sequences of adjoint functors [PDF]

Archiv der Mathematik, 1972
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