Relevant bibliographies by topics / Category FI of finite sets and injections

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  2. Dissertations / Theses

Academic literature on the topic 'Category FI of finite sets and injections'

Author: Grafiati
Published: 7 July 2024

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Journal articles on the topic "Category FI of finite sets and injections"

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Jiao, Pengjie. "The generalized auslander–reiten duality on a module category." Proceedings of the Edinburgh Mathematical Society 65, no. 1 (2022): 167–81. http://dx.doi.org/10.1017/s0013091521000869.

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AbstractWe characterize the generalized Auslander–Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite-dimensional vector spaces with linear injections over a finite field.
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2

Sam, Steven V., and Andrew Snowden. "Representations of categories of G-maps." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 750 (2019): 197–226. http://dx.doi.org/10.1515/crelle-2016-0045.

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Abstract We study representations of wreath product analogues of categories of finite sets. This includes the category of finite sets and injections (studied by Church, Ellenberg, and Farb) and the opposite of the category of finite sets and surjections (studied by the authors in previous work). We prove noetherian properties for the injective version when the group in question is polycyclic-by-finite and use it to deduce general twisted homological stability results for such wreath products and indicate some applications to representation stability. We introduce a new class of formal language
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Dubsky, Brendan. "Incidence Category of the Young Lattice, Injections Between Finite Sets, and Koszulity." Algebra Colloquium 28, no. 02 (2021): 195–212. http://dx.doi.org/10.1142/s1005386721000171.

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We study the quadratic quotients of the incidence category of the Young lattice defined by the zero relations corresponding to adding two boxes to the same row, or to the same column, or both. We show that the last quotient corresponds to the Koszul dual of the original incidence category, while the first two quotients are, in a natural way, Koszul duals of each other and hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather
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4

CHEN, RUIYUAN. "AMALGAMABLE DIAGRAM SHAPES." Journal of Symbolic Logic 84, no. 1 (2019): 88–101. http://dx.doi.org/10.1017/jsl.2018.87.

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AbstractA category has the amalgamation property (AP) if every pushout diagram has a cocone, and the joint embedding property (JEP) if every finite coproduct diagram has a cocone. We show that for a finitely generated category I, the following are equivalent: (i) every I-shaped diagram in a category with the AP and the JEP has a cocone; (ii) every I-shaped diagram in the category of sets and injections has a cocone; (iii) a certain canonically defined category ${\cal L}\left( {\bf{I}} \right)$ of “paths” in I has only idempotent endomorphisms. When I is a finite poset, these are further equiva
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Liu, Ye. "On Chromatic Functors and Stable Partitions of Graphs." Canadian Mathematical Bulletin 60, no. 1 (2017): 154–64. http://dx.doi.org/10.4153/cmb-2016-047-3.

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AbstractThe chromatic functor of a simple graph is a functorization of the chromatic polynomial. M. Yoshinaga showed that two ûnite graphs have isomorphic chromatic functors if and only if they have the same chromatic polynomial. The key ingredient in the proof is the use of stable partitions of graphs. The latter is shown to be closely related to chromatic functors. In this note, we further investigate some interesting properties of chromatic functors associated with simple graphs using stable partitions. Our ûrst result is the determination of the group of natural automorphisms of the chroma
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Mahadevan, Sridhar. "Universal Causality." Entropy 25, no. 4 (2023): 574. http://dx.doi.org/10.3390/e25040574.

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Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories. We present a hierarchical framework called UCLA (Universal Causality Layered Architecture), where at the top-most level, causal interventions are modeled as a higher-order category over simplicial sets and objects. Simplicial sets are contravariant functors from the category of ordinal numbers Δ into sets, and whose morphisms are order-preserving injections and surjections over finite ordered sets. Non-random interventions
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7

Gálvez-Carrillo, Imma, Joachim Kock, and Andrew Tonks. "Decomposition Spaces and Restriction Species." International Mathematics Research Notices 2020, no. 21 (2018): 7558–616. http://dx.doi.org/10.1093/imrn/rny089.

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Abstract We show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital $2$-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce directed restriction species that subsume Schmitt’s restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finite sets and injections, directed restriction species are presheaves on the category of finite posets and co
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8

Richter, Birgit, and Steffen Sagave. "A strictly commutative model for the cochain algebra of a space." Compositio Mathematica 156, no. 8 (2020): 1718–43. http://dx.doi.org/10.1112/s0010437x20007319.

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AbstractThe commutative differential graded algebra $A_{\mathrm {PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal {I}}(X)$ of $A_{\mathrm {PL}}(X)$. Our approach uses diagrams of chain complexes indexed by the category of finite sets and injections $\mathcal {I}$ to model $E_{\infty }$ differential graded algebras (dga) by strictly commutative objects, called commutative $\mathcal {I}$-dgas. We define a functor $A^{\mathcal {I}}$ from simplicial sets to commutative $\mathcal {I}$-dgas
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9

Draisma, Jan, Rob Eggermont, and Azhar Farooq. "Components of symmetric wide-matrix varieties." Journal für die reine und angewandte Mathematik (Crelles Journal), October 25, 2022. http://dx.doi.org/10.1515/crelle-2022-0064.

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Abstract We show that if X n {X_{n}} is a variety of c × n {c\times n} -matrices that is stable under the group Sym ⁡ ( [ n ] ) {\operatorname{Sym}([n])} of column permutations and if forgetting the last column maps X n {X_{n}} into X n - 1 {X_{n-1}} , then the number of Sym ⁡ ( [ n ] ) {\operatorname{Sym}([n])} -orbits on irreducible components of X n {X_{n}} is a quasipolynomial in n for all sufficiently large n. To this end, we introduce the category of affine 𝐅𝐈 𝐨𝐩 {\mathbf{FI^{op}}} -schemes of width one, review existing literature on such schemes, and establish several new structural res
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Sagave, Steffen, and Stefan Schwede. "Homotopy Invariance of Convolution Products." International Mathematics Research Notices, January 8, 2020. http://dx.doi.org/10.1093/imrn/rnz334.

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Abstract The purpose of this paper is to show that various convolution products are fully homotopical, meaning that they preserve weak equivalences in both variables without any cofibrancy hypothesis. We establish this property for diagrams of simplicial sets indexed by the category of finite sets and injections and for tame $M$-simplicial sets, with $M$ the monoid of injective self-maps of the positive natural numbers. We also show that a certain convolution product studied by Nikolaus and the 1st author is fully homotopical. This implies that every presentably symmetric monoidal $\infty $-ca
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Dissertations / Theses on the topic "Category FI of finite sets and injections"

1

Feltz, Antoine. "Foncteurs polynomiaux sur les catégories FId." Electronic Thesis or Diss., Strasbourg, 2024. http://www.theses.fr/2024STRAD002.

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Dans cette thèse on introduit différentes notions (forte et faibles) de foncteurs polynomiaux sur les catégories FId et on étudie leur comportement. On adapte aussi la définition classique de foncteurs polynomiaux (basée sur les effets croisés) au cadre de FId, et on montre que les deux définitions obtenues coïncident. Les foncteurs polynomiaux sur FId s'avèrent plus dificiles à étudier que sur FI. Par exemple, les projectifs standards sont fortement polynomiaux sur FI et on montre que ce n'est plus le cas sur FId pour d > 1. On étudie alors diférents quotients polynomiaux de ces foncteurs.
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