http://www.tac.mta.ca/tac/volumes/37/37/37-37.pdf In category theory, a branch of mathematics, compact closed categories are a general context for treating dual objects. The idea of a dual object generalizes the more familiar concept of the dual of a finite-dimensional vector space. So, the motivating example of a compact closed category is FdVect, the category having finite-dimensional vector spaces as objects and linear maps as morphisms, with tensor product as the monoidal structure. Another example is Rel, the category h…

Crossed Modules and Quantum Groups in Braided Categories

WebOct 16, 2024 · The construction of a model category of coherently compact closed categories leads to a proof of the one dimensional cobordism hypothesis based on a … Web2.3.1 Prof, the compact closed monoidal weak 2-category of categories, profunctors and ... (1963), and the first coherence theorem (namely, that every monoidal category is equivalent to a strict one) was stated and proved by Lane (1963), and this gives a basis for the relationship between string diagrams and monoidal categories. ... oldsilvershed instagram

[1704.02230v2] Coherence for lenses and open games - arXiv.org

WebCOMPACT CLOSED BICATEGORIES MICHAEL STAY Abstract. A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. The unit and counit satisfy the usual “zig-zag” identities of a compact closed category only up to natural isomorphism, and the isomorphism is subject to a … WebOct 18, 2024 · We prove a strictification theorem for cartesian closed bicategories. First, we adapt Power’s proof of coherence for bicategories with finite bilimits to show that every bicategory with bicategorical cartesian closed structure is biequivalent to a 2-category with 2-categorical cartesian closed structure. Weball satisfying certain coherence conditions. Examples ... The canonical example is the category of sets. Compact closed categories are closed categories. The canonical example is the category FdVect with finite-dimensional vector spaces as objects and linear maps as morphisms. More generally, any monoidal closed category is a closed category. isabelle squishmallow