Results 1 to 10 of about 429,595 (233)
Interfacing biology, category theory and mathematical statistics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2020 Motivated by the concept of degeneracy in biology (Edelman, Gally 2001), we establish a first connection between the Multiplicity Principle (Ehresmann, Vanbremeersch 2007) and mathematical statistics. Specifically, we exhibit two families of statistical tests that satisfy this principle to achieve the detection of a signal in noise.
Pastor, Dominique +3 more
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Morita theory and singularity categories [PDF]
, 2020 We propose an analogue of the bounded derived category for an augmented ring spectrum, defined in terms of a notion of Noether normalization. In many cases we show this category is independent of the chosen normalization.
Greenlees, J. P. C., Stevenson, Greg
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Mathematical Morphology via Category Theory
, 2020 Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify the fundamental of morphological operations such as dilation and erosion making use of limit and co-limit preserving
Sharifipour, Hossein Memarzadeh +1 more
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, 2018 Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations.
Marquis, Jean-Pierre
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Quotient completion for the foundation of constructive mathematics [PDF]
, 2013 We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory.
Maietti, Maria Emilia +1 more
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Modalities in homotopy type theory
, 2020 Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes.
Rijke, Egbert +2 more
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Category theory and set theory as theories about complementary types of universals [PDF]
, 2016 Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals.
Ellerman, David P.
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, 2015 The main purpose of this article is to introduce the categorical concept of pullback in Mizar. In the first part of this article we redefine homsets, monomorphisms, epimorpshisms and isomorphisms [7] within a free-object category [1] and it is shown ...
Riccardi, Marco
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The Conformal Characters [PDF]
, 2018 We revisit the study of the multiplets of the conformal algebra in any dimension. The theory of highest weight representations is reviewed in the context of the Bernstein-Gelfand-Gelfand category of modules.
Bourget, Antoine, Troost, Jan
core +5 more sources
Sets in homotopy type theory [PDF]
, 2014 Homotopy Type Theory may be seen as an internal language for the $\infty$-category of weak $\infty$-groupoids which in particular models the univalence axiom.
Rijke, Egbert, Spitters, Bas
core +3 more sources