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On the categorification of homology
Hadrian Heine
https://arxiv.org/abs/2505.22640 https://arxiv.org/pdf/2505.22640

On the categorification of homology
We categorify the concept of homology theories, which we term categorical homology theories. More precisely, we extend the notion of homology theory from homotopy theory to the realm of $(\infty,\infty)$-categories and show that several desirable features remain: we prove that categorical homology theories are homological in a precise categorified sense, satisfy a categorified Whitehead theorem and are classified by a higher categorical analogue of spectra. To study categorical homology theorie…

Order in Partial Markov Categories
Elena Di Lavore, Mario Rom\'an, Pawe{\l} Soboci\'nski, M\'ark Sz\'eles
https://arxiv.org/abs/2507.19424 https://

Order in Partial Markov Categories
Partial Markov categories are a recent framework for categorical probability theory, providing an abstract account of partial probabilistic computation. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically enriched over the category of preordered sets and monotone maps. We show that our construction recovers several well-known order enrichments. We also demonstrate that the existe…

Combat dolls going at it again...
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arxiv_authors: Arxiv authors (1993-2003)
Scientific collaborations between authors of papers submitted to arxiv.org, under 5 categories: gr-qc, astro-ph, cond-mat, hep-ph, and hep-th categories, spanning January 1993 to April 2003. If an author i co-authored a paper with author j, the graph contains a undirected edge from i to j. If the paper is co-authored by k authors this generates a completely connected (sub)graph on k nodes.
This network has 108300 nodes and 186936 edges.

Food's Carbon Footprint - Are you as green as you eat? Your diet has a big impact on carbon footprint. #food #cutCarbon - https://www.

Foods Carbon Footprint
Are you as green as you eat? Your diet has a big impact on carbon footprint. #food #cutCarbon

A Markovian Approach for Cross-Category Complementarity in Choice Modeling
Omar El Housni, Shuo Sun, Rajan Udwani
https://arxiv.org/abs/2508.18566 https://…

A Markovian Approach for Cross-Category Complementarity in Choice Modeling
While single-purchase choice models have been widely studied in assortment optimization, customers in modern retail and e-commerce environments often purchase multiple items across distinct product categories, exhibiting both substitution and complementarity. We consider the cross-category assortment optimization problem where retailers jointly determine assortments across categories to maximize expected revenue. Most prior work on the topic either overlooks complementarity or proposes models t…

arxiv_authors: Arxiv authors (1993-2003)
Scientific collaborations between authors of papers submitted to arxiv.org, under 5 categories: gr-qc, astro-ph, cond-mat, hep-ph, and hep-th categories, spanning January 1993 to April 2003. If an author i co-authored a paper with author j, the graph contains a undirected edge from i to j. If the paper is co-authored by k authors this generates a completely connected (sub)graph on k nodes.
This network has 68746 nodes and 51971 edges.

Food's Carbon Footprint - Are you as green as you eat? Your diet has a big impact on carbon footprint. #food #cutCarbon - https://www.

Foods Carbon Footprint
Are you as green as you eat? Your diet has a big impact on carbon footprint. #food #cutCarbon

arxiv_authors: Arxiv authors (1993-2003)
Scientific collaborations between authors of papers submitted to arxiv.org, under 5 categories: gr-qc, astro-ph, cond-mat, hep-ph, and hep-th categories, spanning January 1993 to April 2003. If an author i co-authored a paper with author j, the graph contains a undirected edge from i to j. If the paper is co-authored by k authors this generates a completely connected (sub)graph on k nodes.
This network has 89209 nodes and 237010 edges.

On the IKEA SMAKLIG Built-in Induction Hob: Review - Is an induction hob better than cooking with gas? How about health and carbon? #induction #cutCarbon #airQuality -

On the IKEA SMAKLIG Built-in Induction Hob: Review
Is an induction hob better than cooking with gas? How about health and carbon? #induction #cutCarbon #airQuality