This is the second in a series of papers detailing the author’s investigations into the intensional type theory of Martin-Löf, as described in Nordström et al. (1990). The first of these papers, Garner (2009), investigated syntactic issues relating to its dependent product types. The present paper is a contribution to its categorical semantics. Seely (1984) proposed that the correct categorical...

background: routine repeat testing of critical laboratory values is very common these days to increase their accuracy and to avoid reporting false or infeasible results. we figure that repeat testing of critical laboratory values has any benefits or not.   methods : we examined 2233 repeated critical laboratory values in 13 different hematology and chemistry tests including: hemoglobin, white b...

Artin glueings of frames correspond to adjoint split extensions in the category and finite-meet-preserving maps. We extend these ideas setting toposes show that a 2-categorical notion 2-category toposes, finite-limit-preserving functors natural transformations. A morphism between is introduced, which allows Ext(H,N) be constructed. contravariantly equivalent Hom(H,N), moreover, this can extende...

A theory of topological gravity is a homotopy-theoretic representation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms. This note describes a relatively accessible example of such a thing, suggested by the wall-crossing formulas of Donaldson theory. 1. Gravity categories A cobordism category has manifolds as objects, and cobordisms as morphisms. Such catego...

Following the results obtained in Preord and in Cat, we characterize the effective étale-descent morphisms inM -Ord, the category ofM -ordered sets for a given monoid M . Furthermore we show that in M -Ord every effective descent morphism is effective for étale-descent (while the converse is false), and we generalize it to a more general context of relational algebras.

We present a game-theoretic model of the polymorphic λ-calculus, system F , as a fibred category. Every morphism σ of the model defines an η-expanded, β-normal form σ̂ of system F whose interpretation is σ. Thus the model gives a precise, non-syntactic account of the calculus.

This is the third paper in a series started in [9]. In it we construct a C-system CC(C, p) starting from a category C together with a morphism p : Ũ → U , a choice of pull-back squares based on p for all morphisms to U and a choice of a final object of C. Such a quadruple is called a universe category. We then define universe category functors and construct homomorphisms of C-systems CC(C, p) d...

We associate a diagrammatic monoidal category $\mathcal{H}\textit{eis}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to symmetric superalgebra $A$, central charge $k \in \mathbb{Z}$, and invertible parameters $z,t$ in some ground ring. When $A$ is trivial, i.e. it equals ring, these categories recover introduced our previous work, when $k$ zero they yield generalizations o...

Abstract Let $${\mathbb {A}}$$ A be a 2-category with suitable opcomma objects and pushouts. We give direct proof that, provided that the codensity monad of morphism p exists is preserved by morphism, factorization given lax descent object two-dimensional cokernel diagram up to isomorphism same as semantic , ...

We study how to obtain partial matchings using the block function Mf, induced by a morphism f between persistence modules. Mf is defined algebraically and linear with respect direct sums of morphisms. some interesting properties provide way obtaining matrix operations.