Enriched duality in double categories: \(\mathcal{V}\)-categories and \(\mathcal{V}\)-cocategories

DOI10.1016/j.jpaa.2018.10.003zbMath1419.18009arXiv1704.00329OpenAlexW2735207601MaRDI QIDQ1730855

Christina Vasilakopoulou

Publication date: 6 March 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.00329

zbMATH Keywords

enriched cocategoriesenriched fibrationenriched matricesfibrant double categorylocally closed monoidal double category

Mathematics Subject Classification ID

Fibered categories (18D30) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Enriched categories (over closed or monoidal categories) (18D20)

Related Items

Monoidal Grothendieck construction ⋮ On measurings of algebras over operads and homology theories ⋮ Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories ⋮ The finite dual coalgebra as a quantization of the maximal spectrum ⋮ Oplax Hopf Algebras ⋮ The coalgebraic enrichment of algebras in higher categories

Cites Work

• Hopf categories
• Monads in double categories
• Enriched categories as a free cocompletion
• Hopf comonads on naturally Frobenius map-monoidales
• Variation through enrichment
• Categorical logic and type theory
• Braided tensor categories
• Monoidal bicategories and Hopf algebroids
• Enrichment through variation
• Category of \(A_\infty\)-categories
• V-cat and V-graph
• Equalizers in the category of cocomplete cocategories
• Fundamental constructions for coalgebras, corings, and comodules.
• Lokal präsentierbare Kategorien. (Locally presentable categories)
• The formal theory of monads
• Double Adjunctions and Free Monads
• A 2-Categories Companion
• On Categories of Monoids, Comonoids, and Bimonoids
• Framed bicategories and monoidal fibrations
• Accessible Categories: The Foundations of Categorical Model Theory
• Introduction to bicategories
• Hopf measuring comonoids and enrichment
• On Enriched Fibrations
• Catégories structurées
• Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads
• Adjoint triangles
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item