ﻻ يوجد ملخص باللغة العربية
Let $mathcal{B}$ be a subcategory of a given category $mathcal{D}$. Let $mathcal{B}$ has monoidal structure. In this article, we discuss when can one extend the monoidal structure of $mathcal{B}$ to $mathcal{D}$ such that $mathcal{B}$ becomes a sub monoidal category of monoidal category $mathcal{D}$. Examples are discussed, and in particular, in an example of loop space, we elaborated all results discussed in this article.
The category of Hilbert modules may be interpreted as a naive quantum field theory over a base space. Open subsets of the base space are recovered as idempotent subunits, which form a meet-semilattice in any firm braided monoidal category. There is a
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an asphericity problem
We introduce DisCoPy, an open source toolbox for computing with monoidal categories. The library provides an intuitive syntax for defining string diagrams and monoidal functors. Its modularity allows the efficient implementation of computational expe
This work is the first one in a series, in which we develop a mathematical theory of enriched (braided) monoidal categories and their representations. In this work, we introduce the notion of the $E_0$-center ($E_1$-center or $E_2$-center) of an enri
For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of $Y$. The f