Results 1 to 10 of about 1,838,152 (282)
Applied Categorical Structures, 2022 AbstractWe introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories.
Enrico Ghiorzi
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Restriction categories as enriched categories
Theoretical Computer Science, 2014 Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its domain, to be thought of as the partial identity that is defined to just the same degree as the original map. In this
Richard Garner, Robin Cockett
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Probabilistic metric spaces as enriched categories [PDF]
Fuzzy Sets and Systems, 2013 In this paper we investigate Cauchy completeness and exponentiablity for quantale enriched categories, paying particular attention to probabilistic metric spaces.
Dirk Hofmann
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Algebras of Higher Operads as Enriched Categories [PDF]
Applied Categorical Structures, 2008 38pp
Mark Weber, Michael Batanin
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The syntactic side of autonomous categories enriched over generalised metric spaces [PDF]
Logical Methods in Computer Science, 2023 Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold.
Fredrik Dahlqvist, Renato Neves
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Cartesian Differential Categories as Skew Enriched Categories [PDF]
Applied Categorical Structures, 2021 AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rigk. However, the tensor product on this category is not the usual one, but
Richard Garner, Jean-Simon Pacaud Lemay
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Enriched Categories of Coalgebras [PDF]
Electronic Journal of MathematicsJean-Paul Mavoungou
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Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory [PDF]
Logical Methods in Computer Science, 2020 We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for
Mathys Rennela, Sam Staton
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Lax orthogonal factorisations in monad-quantale-enriched categories [PDF]
Logical Methods in Computer Science, 2017 We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose ...
Maria Manuel Clementino +1 more
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One dimensional gapped quantum phases and enriched fusion categories
Journal of High Energy Physics, 2022 In this work, we use Ising chain and Kitaev chain to check the validity of an earlier proposal in arXiv:2011.02859 that enriched fusion (higher) categories provide a unified categorical description of all gapped/gapless quantum liquid phases, including ...
Liang Kong, Xiao-Gang Wen, Hao Zheng
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