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An Algebraic Weak Factorisation System from a Dominance
In this chapter we show how the notion of a dominance gives rise to an algebraic weak factorisation system. The left class (coalgebras) of this...
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An Algebraic Weak Factorisation System from a Moore Structure
This chapter shows how an algebraic weak factorisation system can be constructed in a category with Moore structure. Moore structure on a category is...
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Derivation of a Generalised Replicator Equation in the Limit of Weak Selection
The replicator equation is often applied for describing the change in frequency of competing subpopulations, but has only been formally derived under...
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Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators
Let X and Y be two smooth manifolds of the same dimension. It was proved by Seeger et al. in (Ann Math 134(2): 231–251, 1991) that the Fourier...
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The Frobenius Construction
The aim of this chapter is to prove that the algebraic weak factorisation system constructed in Chap. 4...
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Deep Factorisation of the Stable Process III: the View from Radial Excursion Theory and the Point of Closest Reach
We compute explicitly the distribution of the point of closest reach to the origin in the path of any d -dimensional isotropic stable process, with d ...
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Interpreting Node Embedding Distances Through n-Order Proximity Neighbourhoods
In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The...
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Cofibrantly Generated Lax Orthogonal Factorisation Systems
The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems ( awfs s) to cover...
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The Stochastic Gierer–Meinhardt System
The Gierer–Meinhardt system occurs in morphogenesis, where the development of an organism from a single cell is modelled. One of the steps in the...
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Equip** weak equivalences with algebraic structure
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that...
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Internal neighbourhood structures
The main aim of this paper is to provide a description of neighbourhood operators in finitely complete categories with finite coproducts and a proper...
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Preliminaries
In this chapter we introduce the main theoretical framework in which our theory of effective fibrations is embedded. Abstractly put, we are studying...
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Analysis of parametric models
Parametric models in vector spaces are shown to possess an associated linear map, leading directly to reproducing kernel Hilbert spaces and...
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Modified Surgery
In this chapter we digress from the main line of the book, which treats the classification of manifolds with a given homotopy type via classical...
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Abundance theorem for threefolds in mixed characteristic
We prove the abundance theorem for arithmetic klt threefold pairs whose closed point have residue characteristic greater than 5. As a consequence, we...
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Introduction
The main contribution of this book is the introduction of the concept of an effective Kan fibration. So what is our notion of an effective Kan...
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Conclusion
In this final chapter we would like to take stock of the properties of effective Kan fibrations that we have established and outline some directions...
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Classification of singular del Pezzo surfaces over finite fields
In this article, we consider weak del Pezzo surfaces defined over a finite field, and their associated, singular, anticanonical models. We first...
