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The Theory Of Categories
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The the theory of categories is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.Abstract:
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Citations
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Journal ArticleDOI
Categorification of persistent homology
Peter Bubenik,Jonathan A. Scott +1 more
TL;DR: In this paper, the main objects of study are diagrams, indexed by the poset of real numbers, in some target category, and the set of such diagrams has an interleaving distance which generalizes the previously-studied bottleneck distance.
Journal ArticleDOI
Generalized persistence diagrams
TL;DR: In this article, the authors generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category.
Dissertation
Fabricating Architecture : from modern to global space
TL;DR: Tese de Doutoramento em Arquitectura apresentada a Faculdade de Ciencias e Tecnologia da Universidade de Coimbra as discussed by the authors
Journal ArticleDOI
Affine highest weight categories and affine quasihereditary algebras
TL;DR: In this article, an affine analogue of the Cline-Parshall-Scott Theorem was proved for affine cellular algebras, and the notions of affine quasihereditary algebra and affine highest weight category were studied.
Journal ArticleDOI
The fundamental: Ungrounded or all-grounding?
TL;DR: It is argued that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground, and the door is opened to recognising a bifurcation in the notion of fundamentality.
References
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Journal ArticleDOI
Categorification of Persistent Homology
Peter Bubenik,Jonathan A. Scott +1 more
TL;DR: This work redevelops persistent homology (topological persistence) from a categorical point of view and gives a natural construction of a category of ε-interleavings of $\mathbf {(\mathbb {R},\leq)}$-indexed diagrams in some target category and shows that if the target category is abelian, so is this category of interleavments.
Journal ArticleDOI
Generalized persistence diagrams
TL;DR: In this article, the authors generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category.
Dissertation
Fabricating Architecture : from modern to global space
TL;DR: Tese de Doutoramento em Arquitectura apresentada a Faculdade de Ciencias e Tecnologia da Universidade de Coimbra as discussed by the authors
Journal ArticleDOI
The fundamental: Ungrounded or all-grounding?
TL;DR: It is argued that Dichotomy fails: some facts have partial grounds that cannot be complemented to a full ground, and the door is opened to recognising a bifurcation in the notion of fundamentality.
Posted Content
The Jordan-H\"older property and Grothendieck monoids of exact categories
TL;DR: In this paper, it was shown that the Jordan-Holder property (JHP) holds in an exact category if and only if the Grothendieck monoid introduced by Berenstein and Greenstein is free.