3 Citations
Differential 2-rigs
- Mathematics
- 2021
We propose the notion of differential 2-rig, a category R equipped with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor m : R → R that satisfies a…
Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages
- Mathematics, Computer ScienceProc. ACM Program. Lang.
- 2022
This paper gives a denotational semantics for the Pi family of reversible programming languages for boolean circuits, using weak groupoids à la Homotopy Type Theory, and shows how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of type isomorphisms.
Sheet diagrams for bimonoidal categories
- Mathematics
- 2020
Bimonoidal categories (also known as rig categories) are categories with two monoidal structures, one of which distributes over the other. We formally define sheet diagrams, a graphical calculus for…
References
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- Mathematics
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This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the…
∞-Categories for the Working Mathematician
- Mathematics
- 2018
homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,…
Handbook Of Categorical Algebra 1 Basic Category Theory
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Category theory is the key to a clear presentation of modern abstract "Basic Category Theory for Computer Scientists" by Benjamin C. Pierce (1991). "Handbook of Categorical Algebra" by Francis…
Quantum Groups
- Mathematics
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This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…
E∞ ring spaces and E∞ ring spectra
- Mathematics
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? functors.- Coordinate-free spectra.- Orientation theory.- E? ring spectra.- On kO-oriented bundle theories.- E? ring spaces and bipermutative categories.- The recognition principle for E? ring…
STRICTIFICATION OF CATEGORIES WEAKLY ENRICHED IN SYMMETRIC MONOIDAL CATEGORIES
- Mathematics
- 2009
We show that categories weakly enriched over symmetric monoidal cate- gories can be strictied to categories enriched in permutative categories. This is a \many 0-cells" version of the strictication…
Icons
- Physics
- 2008
THE EXPERIMENT ITSELF The understanding of the origin of life was largely speculative until the 1920s, when Oparin and Haldane, working independently, proposed a theoretical model for “chemical…
Coherence for distributivity
- Mathematics
- 1972
Miquel L. Laplaza University of Chicago and University of Puerto Rico at Mayaguez Received November 5, 197
Monoidal Functors
- Species and Hopf Algebras. CRM Monographs Series, vol. 29, American Mathematical Society
- 2010