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Simplicial Databases
[article]

2009
*
arXiv
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pre-print

*I*

*I*

*I*f * U X U f U Y . ... For an object

*i*∈

*I*, we denote the database X (

*i*) by X

*i*and write X

*i*= (X

*i*, K

*i*, τ

*i*). To define the colimit (respectively limit) of the diagram X , we must first specify its schema. ...

##
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Kleisli Database Instances
[article]

2012
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arXiv
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pre-print

To make this precise, we will say that a tunable monad is a pair (

arXiv:1209.1011v1
fatcat:qhhtt4tllbaqfow6avgjrctnzu
*I*, P q where*I*is a small category and P :*I*Ñ Monad Set is a functor (see Definition 5.1.3). ... So for any morphism f :*i*Ñ*i*1 in*I*and any schema C we have a functor C-KlspP piqq Ñ C-KlspP pi 1 qq that functorially converts P piq-instances into P pi 1 q-instances. ...##
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Dirichlet Functors are Contravariant Polynomial Functors
[article]

2020
*
arXiv
*
pre-print

Myers was supported by the National Science Foundation grant DMS-1652600, and

arXiv:2004.04183v1
fatcat:x2xmv7353jgkjdk7ma6wgdktgm
*Spivak*was supported by AFOSR grants FA9550-19-1-0113 and FA9550-17-1-0058. ... It remains to show, then, that the map of bundles colim X*i*colim X*i*colim 1 1 is an isomorphism in Set ↓ , for which it suffices to show that colim 1 is terminal. ...##
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Table manipulation in simplicial databases
[article]

2010
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arXiv
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pre-print

If

arXiv:1003.2682v1
fatcat:nwq5jmhawnbl3ee4yatmq54f44
*i*: σ ⊂ σ ′ is a subsimplex, we need functors F (*i*) : Tables σ ′ → Tables σ and G(*i*) : Tables σ → Tables σ ′ . These are the pullback and push-forward functors F (*i*) :=*i** and G(*i*) :=*i*+ . ... The functor F (*i*) sends τ ′ to the bottom row in the commutative diagram K ′ τ ′ / / Γ(σ ′ )*i** K ′*i** •τ / / Γ(σ). ...##
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Higher-dimensional models of networks
[article]

2009
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arXiv
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pre-print

Proposition

arXiv:0909.4314v1
fatcat:uv2zzjf6mzgznjz65gn7hjzpfi
*I*), where*I*is a category and f : ∆ B →*I*is a functor. We may denote (*I*, ∆ B f − →*I*) simply by*I*, if f is clear from context. ... Note that R*i*• L*i*: G → G takes any graph to itself, but the functor L*i*• R*i*: H → H destroys information. ...##
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Regular and relational categories: Revisiting 'Cartesian bicategories I'
[article]

2019
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arXiv
*
pre-print

for each m, n ∈ N, and (iii) the following diagrams commute for every c, d ∈ C and µ : m → n in P: c ⊗m ⊗ d ⊗m c ⊗n ⊗ d ⊗n (c ⊗ d) ⊗m (c ⊗ d) ⊗n s c (µ)⊗s d (µ) σ σ s c⊗d (µ)

arXiv:1909.00069v1
fatcat:tp645obuovdsxhqmzqvrxhgldi
*I**I**I*⊗m*I*⊗n σ σ s*I*(µ) ... This proves (*i*). ...##
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QINL: Query-integrated Languages
[article]

2015
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arXiv
*
pre-print

{x.1} : Set T 1 × :=

arXiv:1511.06459v1
fatcat:4v5byo76jzc2rahmstykdiyalq
*I*: (Set T 1 ) × (Set T 2 ) ⊢ for x 1 ∈*I*.1. for x 2 ∈*I*.2. ... Then an instance*I*on this schema consists of, for each T ∈ T , a set*I*(T ), and for each E : T 1 → T 2 ∈ E, a function*I*(T ) :*I*(T 1 ) →*I*(T 2 ), such that all equations of C are true in*I*. ...##
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Who Sings the Nation-State?, Judith Butler and Gayatri Chakravorty Spivak

2009
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Lectora: Revista de Dones i Textualitat
*

*DAVID*LAGUARDIA Dartmouth College ... So then, finally,

*I*want to think about efficacious speech, and how in certain kinds of political speech, assertions and declarations constitute a certain kind of wager. (55) In contrast to the efficacy ...

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Behavioral Mereology (Proofs and Properties)
[article]

2020
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arXiv
*
pre-print

Generally, if a

arXiv:1811.00420v2
fatcat:cx3ag3kr3beqtjwtbx4xwi5jgq
*i*∈ P*i*is some family of behaviors indexed by a set*I*, then this family is said to be compatible if there is an s ∈ S such that s Pi = a*i*for all*i*∈*I*. ... The join has behaviors B X∪Y = {(f, g) ∈ R[x, y]/*I*× R[x, y]/J | ∃h ∈ R[x, y]. h +*I*= f +*I*and h + J = g + J} = {(h +*I*, h + J) | h ∈ R[x, y]}. ...##
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Hypergraph Categories
[article]

2019
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arXiv
*
pre-print

The above operadic viewpoint on wiring diagrams was put forth by

arXiv:1806.08304v3
fatcat:vqwwgtw2knacbpcqku45rpyf3i
*Spivak*and collaborators [Spi13; RS13; VSL15]. ... Simultaneously,*Spivak*defined essentially the same structure in his work on databases [Spi13] , but preferred a more uniform, combinatorial approach. ... The hypergraph category H A H has the same objects as H and has homsets H A H (X, Y ) = H(*I*, X ⊕Y ). ...##
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Algebraic Databases
[article]

2016
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arXiv
*
pre-print

In [Spi12] ,

arXiv:1602.03501v2
fatcat:h3562zannbgeplfe2sjchi4z4i
*Spivak*puts emphasis on the ability to move data from one format, or database schema, to another. ... Rosebrugh et al. formalized attributes in terms of infinite coproducts of a chosen terminal object, whereas*Spivak*formalized them by slicing the category of copresheaves over a fixed object. ...##
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Dirichlet Polynomials form a Topos
[article]

2020
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arXiv
*
pre-print

*Spivak*also appreciates support by Honeywell Inc. as well as AFOSR grants FA9550-17-1-0058 and FA9550-19-1-0113. ... P P(1)

*i*1 P × P(1) '

*i*′ and D D(0)

*i*1 D × D(0) '

*i*′ . Remark 3.5. ... And given a function π : s → t, define D π ≔ t

*i*1 (d

*i*) y , where d

*i*≔ π −1 (

*i*) for each 1 ≤

*i*≤ t. (N.B. ...

##
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Categorical Data Integration for Computational Science
[article]

2019
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arXiv
*
pre-print

Categorical Query Language is an open-source query and data integration scripting language that can be applied to common challenges in the field of computational science. We discuss how the structure-preserving nature of CQL data migrations protect those who publicly share data from the misinterpretation of their data. Likewise, this feature of CQL migrations allows those who draw from public data sources to be sure only data which meets their specification will actually be transferred. We

arXiv:1903.10579v1
fatcat:idsg7exy7jazjbtudjskezigxq
## more »

... some open problems in the field of data sharing in computational science are addressable by working within this paradigm of functorial data migration. We demonstrate these tools by integrating data from the Open Quantum Materials Database with some alternative materials databases.##
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Functorial data migration

2012
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Information and Computation
*

: S = 101 • First ) ) Last

doi:10.1016/j.ic.2012.05.001
fatcat:sumnhl6bznc6bcwh4x35jgpcaq
*I**I*Mgr a a isIn A A 102 • 103 • q10 • x02 • Secr h h Name | | Alan • Hilbert • Production • Bertrand • Russell • Sales •*David*• Turing • π (12) C = Employee • isIn G G Mgr ... SSN First Last Salary T1-001 115-234 Bob Smith T1-001.Salary T1-002 122-988 Sue Smith T1-002.Salary T1-003 198-877 Alice Jones T1-003.Salary T2 : Employee ID First Last Mgr isIn 101*David*...##
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Functorial aggregation
[article]

2022
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arXiv
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pre-print

In the next sections

arXiv:2111.10968v4
fatcat:kzk2x2dvynffrkhvs5rsqewoze
*I*will introduce these structures, but before leaving the introduction*I*want to say why aggregation was so difficult to get right. ... ♦ We learned the following from*David*Jaz Myers. Proposition 2.1.18. For any ∈ Poly, there is a natural comonoid structure on . Proof. ...
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