2021/08/15 by Yves Fomatati, Fomatati, Yves
Mathematics · #15A23 #15A69 #18A05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2108.06690
openalex publication_date 2021/08/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The notion of semi-unital semi-monoidal category was defined a couple of\nyears ago using the so called "Takahashi tensor product" and so far, the only\nexample of it in the literature is complex. In this paper, we use the recently\ndefined "multiplicative tensor product of matrix factorizations" to give a\nsimple example of this a notion. In fact, if MF(1) denotes the category of\nmatrix factorizations of the constant power series 1, we define the concept\nof one-step connected category and prove that there is a one-step connected\nsubcategory of (MF(1), widetilde\⊗) which is semi-unital\nsemi-monoidal. We also define the concept of right pseudo-monoidal category\nwhich generalizes the notion of monoidal category and we prove that\n(MF(1), widetilde\⊗) is an example of this concept.\n