Finite Products are Biproducts in a Compact Closed Category

If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.Comment: 9 pages. Introduction further expanded, minor errors correcte

Addressing Disproportionality in School Discipline through Universal School-WidePositive Behavior Support

Suspensions are the most commonly used discipline strategy in schools and in many cases these lead to poor academic and behavioral outcomes for students. Suspensions are also implemented inconsistently as a consequence of disciplinary infractions; this has resulted in the disproportionate suspension rates of minority and special education students. Recently, school-wide Positive Behavior Support (SWPBS) has emerged as an alternative model to suspension. SWPBS is a proactive, school-wide approach to discipline, which focuses on teaching and reinforcing appropriate behavior to all students. The purpose of the current study is to examine the effectiveness of SWPBS on reducing disproportionate rates of suspension. Current suspension rates of a Maryland school implementing SPWBS were compared with baseline suspension rates prior to the implementation of the program. Specifically, the suspension rates of ethnic minority students and students with disabilities were analyzed to determine if the implementation of SWPBS resulted in a decrease in the suspension rates of these populations of students. Findings from the current study indicate that although universal SWPBS strategies are effective in reducing the overall out-of-school suspension rate of the student population, they are less effective for ethnic minority students and students with disabilities.Implications for schools and future research are discussed

Representation Matters: One Approach to Centering Diversity in Science Classes | Speaker Series

While some disciplines lend themselves to a focus on DEI issues via the content of the courses themselves, math and science courses historically do not. As we all work to make our classrooms more inclusive and accessible, we can benefit from observing and discussing approaches others have taken. Please join us for a discussion of one approach to centering DEI efforts in a STEM field and stay for a mini-conference that has emerged from this work

Creativity in Teaching - Engaging Students | Brownbag Series

Bring your lunch and learn from your colleagues! Brownbag lunch presentations will be held four times this semester with different faculty members presenting topics that may be helpful to you

An Investigation of Early Literacy Outcomes by Socio-Economic Status and Race/Ethnicity

The purpose of this study was to examine the early literacy outcomes of children prior to school entry and describe the magnitude of outcome and experiential differences by socio-economic status (SES) and racial/ethnic groups. In addition, I examined the extent to which SES, race/ethnicity, child, home, and early care/education factors and experiences explained early literacy outcomes. My study was an extension of research conducted by Lee and Burkam (2002) about early literacy outcomes at kindergarten entry. I used the full sample data from the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B), a study of a nationally representative sample of children in the United States. The results of this study show large gaps in the 48-month early literacy scores when examined by SES and a wide variation in child experiences prior to school entry. The findings suggest a need for specific and targeted consideration of group outcomes when revising, creating, and funding federal early childhood policies that are designed to improve group early literacy outcomes prior to school entry

Abstract Tensor Systems as Monoidal Categories

The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract tensor system and demonstrate the construction of its associated category. We then show that the associated category of the free abstract tensor system is in fact the free traced symmetric monoidal category on a monoidal signature. A notable consequence of this result is a simple proof for the soundness and completeness of the diagrammatic language for traced symmetric monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda

Spherical Categories

This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras and the motivating application is the definition of 6j-symbols as used in topological field theories. We introduce the new notion of a spherical category. In the first section we prove a coherence theorem for a monoidal category with duals following MacLane (1963). In the second section we give the definition of a spherical category, and construct a natural quotient which is also spherical. In the third section we define spherical Hopf algebras so that the category of representations is spherical. Examples of spherical Hopf algebras are involutory Hopf algebras and ribbon Hopf algebras. Finally we study the natural quotient in these cases and show it is semisimple.Comment: 16 pages. Minor correction

A Quillen model structure for Gray-categories

A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of Gray-groupoids. This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types. The model structure on Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of tricategories and strict homomorphisms of tricategories.Comment: v2: fuller discussion of relationship with work of Berger; localizations are done directly with simplicial set

What is a categorical model of arrows?

We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow equivalent. In this paper, we show that the situation is more subtle. By considering Arrows wholly within the base category we derive two alternative formulations of Freyd category that are equivalent to Arrows—enriched Freyd categories and indexed Freyd categories. By imposing a further condition, we characterise those indexed Freyd categories that are isomorphic to Freyd categories. The key differentiating point is the number of inputs available to a computation and the structure available on them, where structured input is modelled using comonads