Related papers: Adjunction and inversion of adjunction

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

We extend results of our previous papers, on ordinary multiple points of curves, and on the computation of their conductor, to ordinary multiple subvarieties of codimension one.

This paper presents equations for the inverse of a Clifford number in Clifford algebras of up to five dimensions. In presenting these, there are also presented formulas for the determinant and adjugate of a general Clifford number of up to…

We make precise the structure of the first two reduction morphisms associated with codimension two nonsingular subvarieties of quadrics $\Q{n}$, $n\geq 5$. We give a coarse classification of the same class of subvarieties when they are…

A complete proof is given of relative interpretability of Adjunctive Set Theory with Extensionality in an elementary concatenation theory.

Upper moduli part of adjunction is introduced and its basic property are discussed. The moduli part satisfies the BP in the case of rational multiplicities and is nef in the maximal case.

We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.

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…

This is a first instalment of much larger work about relations between birational geometry and moduli of triples. The extraction of work is mainly related to Theorem 6. It is a weak version of Kawamata's Conjecture 1 and an important…

Given an adjunction connecting reasonable categories with weak equivalences, we define a new derived bar and cobar construction associated to the adjunction. This yields homotopical models of the completion and cocompletion associated to…

Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general…

Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct…

We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the…

We construct an explicit combinatorial model of the functor which adds right adjoints to the morphisms of an $\infty$-category, and we speculate on possible extensions to higher dimensions.

In this paper we study singularities defined by the action of Frobenius in characteristic $p > 0$. We prove results analogous to inversion of adjunction along a center of log canonicity. For example, we show that if $X$ is a Gorenstein…

In the present work, a natural sequel to \cite{MaPi1}, we further discuss the existence of adjunctions between categories of institutions and of $\pi$-institutions. This is done at both a foundational and an applied level. Firstly, we…

In this paper, we construct counterexamples to the boundedness of generalised log canonical models of surfaces with fixed appropriate invariants, where the underlying varieties can have arbitrary Kodaira dimension. This answers a question…

The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with $\mathbb{R}$-coefficients). This complements Filipazzi's canonical bundle formula for morphisms with connected fibres. It is then…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.