Tootfinder

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Colimits of Heyting Algebras through Esakia Duality
Rodrigo Nicolau Almeida

$G\operatorname{-CGWH}$ spaces and their (homotopy) colimits
Aleksandar Miladinovi\'c
https://arxiv.org/abs/2508.19037 https://arxiv.org/pdf/2508.19037…

$G\operatorname{-CGWH}$ spaces and their (homotopy) colimits
In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group $G$ together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy) colimits and mapping spaces, and consequently, homotopy groups.

Hilbert spaces admit no finitary discrete imaginaries
Ruiyuan Chen, Isabel Trindade
https://arxiv.org/abs/2509.11321 https://arxiv.org/pdf/2509.11321

Hilbert spaces admit no finitary discrete imaginaries
We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially constant on all infinite-dimensional spaces. In other words, every finitary set-valued imaginary over the theory of Hilbert spaces, in a broad signature-independent sense, must be essentially trivial. This extends a result and answers a question by Lieberman--Rosický--Vasey, who showed that no such functor on the supercate…

A Category Theory Framework for Macroeconomic Modeling: The Case of Argentina's Bimonetary Economy
Luciano Pollicino
https://arxiv.org/abs/2508.13233 https://

A Category Theory Framework for Macroeconomic Modeling: The Case of Argentina's Bimonetary Economy
Traditional macroeconomic models, based on static algebraic systems, fail to capture the dynamics of a bimonetary economy like Argentina's. This paper proposes a framework based on category theory to develop a more flexible and structured model that represents the evolving relationships between key variables such as inflation expectations, interest rates, and currency demand. Using concepts like objects, morphisms, learning/forgetful functors, limits, and colimits, the model is applied to empir…

The derivator of a dg-category
Francesco Genovese, Chiara Sava, Jan \v{S}\v{t}ov\'i\v{c}ek
https://arxiv.org/abs/2508.02612 https://arxiv.org/pdf/2508.…

The derivator of a dg-category
In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exac…

Open 2D TFTs admit initial open-closed extensions
Shaul Barkan, Jan Steinebrunner, Adela YiYu Zhang
https://arxiv.org/abs/2509.02553 https://arxiv.org/pdf/…

Open 2D TFTs admit initial open-closed extensions
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology object of its value at the disk. As a corollary, we obtain an action of the moduli spaces of surfaces on the Hochschild homology object of $E_1$-Calabi-Yau algebras. This provides a space level refinement of previous work of Costello over $\mathbb{Q}$ and Wahl…

Existence Theorem for Cumulative Universe Towers and Its Applications
Higuchi Joaquim Reizi
https://arxiv.org/abs/2506.21653 https://…

Existence Theorem for Cumulative Universe Towers and Its Applications
This paper builds a cumulative tower of Grothendieck universes that provides a precise size discipline for higher type theory. Starting from an increasing sequence of inaccessible cardinals, we give an inductive-recursive definition of universe codes, their decoding functor, and a rank that controls the growth of each code. For every level of the tower we prove closure under dependent products, dependent sums, identity types, and all finite limits and colimits; the colimit part is obtained with…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Coslice Colimits in Homotopy Type Theory
Perry Hart (Favonia), Kuen-Bang Hou (Favonia)

Large condensation in enriched $\infty$-categories
Devon Stockall
https://arxiv.org/abs/2506.23632 https://arxiv.org/pdf/2506.23632…

Large condensation in enriched $\infty$-categories
Using the language of enriched $\infty$-categories, we formalize and generalize the definition of fusion n-category, and an analogue of iterative condensation of $E_i$-algebras. The former was introduced by Johnson-Freyd, and the latter by Kong, Zhang, Zhao, and Zheng. This extends categorical condensation beyond fusion n-categories to all enriched monoidal $\infty$-categories with certain colimits. The resulting theory is capable of treating symmetries of arbitrary dimension and codimension th…