Category Theory

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New submissions for Fri, 10 May 24

[1]  arXiv:2405.05774 [pdf, ps, other]

Title: Monoidal bicategories, differential linear logic, and analytic functors

Authors: M. Fiore, N. Gambino, M. Hyland

Comments: v1. 46 pages. Comments welcome

Subjects: Category Theory (math.CT); Logic in Computer Science (cs.LO); Logic (math.LO)

We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear explonential comonad, as considered in the study of linear logic, and of a codereliction transformation, introduced to study differential linear logic via differential categories. As an application, we extend the differential calculus of Joyal's analytic functors to analytic functors between presheaf categories, just as ordinary calculus extends from a single variable to many variables.

Replacements for Fri, 10 May 24

[2]  arXiv:2012.15431 (replaced) [pdf, ps, other]

Title: Exact categories of topological vector spaces with linear topology

Authors: Leonid Positselski

Comments: LaTeX 2e with xy-pic; 71 pages, 9 commutative diagrams; v.2: Remark 12.2, Example 13.1(3), and Remark 13.6 inserted; v.3: seven references added; v.4: several misprints corrected, references added and updated, two paragraphs inserted in the Introduction, one in Example 4.1, and one in Section 9; v.5: several misprints corrected

Subjects: Category Theory (math.CT); General Topology (math.GN)

[3]  arXiv:2110.14576 (replaced) [pdf, ps, other]

Title: Kripke-Joyal forcing for type theory and uniform fibrations

Authors: S. Awodey, N. Gambino, S. Hazratpour

Comments: v2. 56 pages. Minor changes following referee report. To appear in Selecta Mathematica, New Series

Subjects: Logic (math.LO); Category Theory (math.CT)

[4]  arXiv:2210.06279 (replaced) [pdf, ps, other]

Title: The moment problem for random objects in a category

Authors: Will Sawin, Melanie Matchett Wood

Comments: 71 pages

Subjects: Probability (math.PR); Category Theory (math.CT)

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