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Metric enrichment, finite generation, and the path coreflection

Alexandru Chirvasitu (2024)

Archivum Mathematicum

We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally 1 -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry- 0 -generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...

Modular operads with connected sum and Barannikov’s theory

Lada Peksová (2020)

Archivum Mathematicum

We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.

Modules.

Cockett, J. R. B., Koslowski, J., Seely, R. A. G., Wood, R. J. (2003)

Theory and Applications of Categories [electronic only]

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