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Simplicial Databases [article]

David I. Spivak
2009 arXiv   pre-print
I I I f * U X U f U Y .  ...  For an object iI, 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.  ...

Kleisli Database Instances [article]

David I. Spivak
2012 arXiv   pre-print
To make this precise, we will say that a tunable monad is a pair (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.  ...

Dirichlet Functors are Contravariant Polynomial Functors [article]

David Jaz Myers, David I. Spivak
2020 arXiv   pre-print
Myers was supported by the National Science Foundation grant DMS-1652600, and 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.  ...

Table manipulation in simplicial databases [article]

David I. Spivak
2010 arXiv   pre-print
If 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).  ...

Higher-dimensional models of networks [article]

David I. Spivak
2009 arXiv   pre-print
Proposition 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.  ...

Regular and relational categories: Revisiting 'Cartesian bicategories I' [article]

Brendan Fong, David I Spivak
2019 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) I I I ⊗m I ⊗n σ σ s I (µ)  ...  This proves (i).  ...

QINL: Query-integrated Languages [article]

Patrick Schultz, David I. Spivak, Ryan Wisnesky
2015 arXiv   pre-print
{x.1} : Set T 1 × := 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.  ...

Who Sings the Nation-State?, Judith Butler and Gayatri Chakravorty Spivak

David Laguardia
2009 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  ...

Behavioral Mereology (Proofs and Properties) [article]

Brendan Fong, David Jaz Myers, David I. Spivak
2020 arXiv   pre-print
Generally, if a 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 iI.  ...  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]}.  ...

Hypergraph Categories [article]

Brendan Fong, David I Spivak
2019 arXiv   pre-print
The above operadic viewpoint on wiring diagrams was put forth by 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 ).  ...

Algebraic Databases [article]

Patrick Schultz, David I. Spivak, Christina Vasilakopoulou, Ryan Wisnesky
2016 arXiv   pre-print
In [Spi12] , 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.  ...

Dirichlet Polynomials form a Topos [article]

David I. Spivak, David Jaz Myers
2020 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.  ...

Categorical Data Integration for Computational Science [article]

Kristopher Brown, David I. Spivak, Ryan Wisnesky
2019 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
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.

Functorial data migration

David I. Spivak
2012 Information and Computation
: S = 101 • First ) ) Last 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  ...

Functorial aggregation [article]

David I. Spivak
2022 arXiv   pre-print
In the next sections 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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