Faculty Consultations: An Extra Dimension to the University of Wyoming Writing Center

Do we not have enough to do when consulting with students? Why reach out to faculty? The simple answer is that we feel our writing center work is accomplished in collaboration with both faculty and students. It is a center for everyone to talk about writing. The more complex answer is that many benefits are realized by working with faculty as well as students. One direct benefit is that we remove the stigma that the Writing Center is a place for poor writers, a place primarily for remediation. When we give classroom introduction talks, we can honestly say that we work with writers at all levels on all kinds of writing. We mention that we work with faculty as well as graduate and undergraduate students, and that the staff members make appointments with one another. When freshmen arrive at our door, they should not feel they are there because they are problem writers. We want people on our campus to know that everyone can benefit from talking about writing in our writing center, and working with faculty helps get across that idea.University Writing Cente

Combinatorial structure of type dependency

We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf category. The objects of the presheaf category encode the basic judgements of a dependent sequent calculus, while the action of the monad encodes the deduction rules; so by giving an explicit description of the monad, we obtain an explicit account of the combinatorics of type dependency. We find that this combinatorics is controlled by a particular kind of decorated ordered tree, familiar from computer science and from innocent game semantics. Furthermore, we find that the monad at issue is of a particularly well-behaved kind: it is local right adjoint in the sense of Street--Weber. In future work, we will use this fact to describe nerves for dependent type theories, and to study the coherence problem for dependent type theory using the tools of two-dimensional monad theory.Comment: 35 page

The Isbell monad

In 1966, John Isbell introduced a construction on categories which he termed the "couple category" but which has since come to be known as the Isbell envelope. The Isbell envelope, which combines the ideas of contravariant and covariant presheaves, has found applications in category theory, logic, and differential geometry. We clarify its meaning by exhibiting the assignation sending a locally small category to its Isbell envelope as the action on objects of a pseudomonad on the 2-category of locally small categories; this is the Isbell monad of the title. We characterise the pseudoalgebras of the Isbell monad as categories equipped with a cylinder factorisation system; this notion, which appears to be new, is an extension of Freyd and Kelly's notion of factorisation system from orthogonal classes of arrows to orthogonal classes of cocones and cones.Comment: 21 page

Two-dimensional models of type theory

We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.Comment: 46 pages; v2: final journal versio

Cultural justice and ethics: From within

Where I eventually got a lot of support, awhi, aroha, was from the PPTA when I became a member of Te Huarahi and they helped to see me through the tears and the confusion. It wasn’t because I was Maori, it was because I was a human being. I think the process I have gone through is a process of becoming human, and becoming real in thinking; yes, my experience is valid. I’m not just Maori, I’m Pakeha too. I want both of them, I am both of them. I don’t have to get up and speak fluent Maori right now. Perhaps it will come. I hope it does because I want it to, and I’m going to work on it. But I do feel that people like me, and there are many of us, are not marginal. We are bridges between cultures. This diversity has to be acknowledged, honoured and respected

Magnetic heading reference

This invention employs a magnetometer as a magnetic heading reference for a vehicle such as a small aircraft. The magnetometer is mounted on a directional dial in the aircraft in the vicinity of the pilot such that it is free to turn with the dial about the yaw axis of the aircraft. The invention includes a circuit for generating a signal proportional to the northerly turning error produced in the magnetometer due to the vertical component of the earth's magnetic field. This generated signal is then subtracted from the output of the magnetometer to compensate for the northerly turning error