An interpretation of dependent type theory in a model category of locally cartesian closed categories

Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original interpretation in an individual lcc category can then be recovered by slicing. As in the original interpretation, we face the issue of coherence: Categorical structure is usually preserved by functors only up to isomorphism, whereas syntactic substitution commutes strictly with all type-theoretic structures. Our solution involves a suitable presentation of the higher category of lcc categories as model category. To that end, we construct a model category of lcc sketches, from which we obtain by the formalism of algebraically (co)fibrant objects model categories of strict lcc categories and then algebraically cofibrant strict lcc categories. The latter is our model of dependent type theory.

Homotopy theory of Moore flows (I)

A reparametrization category is a small topologically enriched symmetric semimonoidal category such that the semimonoidal structure induces a structure of a commutative semigroup on objects, such that all spaces of maps are contractible and such that each map can be decomposed (not necessarily in a unique way) as a tensor product of two maps. A Moore flow is a small semicategory enriched over the closed semimonoidal category of enriched presheaves over a reparametrization category. We construct the q-model category of Moore flows. It is proved that it is Quillen equivalent to the q-model category of flows. This result is the first step to establish a zig-zag of Quillen equivalences between the q-model structure of multipointed d-spaces and the q-model structure of flows.

When learning how to lead, an exploratory look at role models

PurposeThe purpose of this study is to identify who people indicate are their role models for learning how to lead and explore how demographic characteristics may affect these choices.Design/methodology/approachA global online survey, involving over 34,000 respondents, indicated, from a list of 14 possibilities, the role model category from whom they learned to lead. Respondents indicated their age, gender, ethnicity, nationality, educational level, hierarchical level and job function. Chi-square analysis was used to identify how these factors may have affected the choice of role models distribution.FindingsFamily member (parents, siblings and other family outside of the immediate family) was found to be the most important role model category when it came to learning how to lead. Ranked second was immediate supervisor/manager. The rank order in terms of frequency of role model choices was not substantially different across demographic characteristics, though there were statistically significant differences regarding the relative importance of the various role model categories by demographics.Research limitations/implicationsThe results offer plentiful opportunities for future scholars to delve more into both the nature and actions of role models, in keeping with social learning theory. Future scholars can investigate the nature of people's relationships with leadership role models, especially conceptualizing why and how various demographic factors affect how people learn to lead.Practical implicationsUnderstanding who people have as role models for what they have learned about leadership can provide important insights for those responsible for leadership development. Similarly, individuals who are in role model “positions” (e.g. parents, teachers, managers) can be more aware of how their behaviors have implications for how their audience learns what effective leadership looks like in action.Originality/valueThis study addressed a relatively unexplored area in the leadership literature, namely within what category of role model have people found to be most important in helping them learn to lead. The large and diverse sample, across a multitude of demographic characteristics, strengthens the generalizability of the findings.

ESTIMATES OF SUBSISTENCE MINIMUM BASKETS AND SOCIAL MINIMUM BASKETS FOR 2019

The article presents estimates of Subsistence minimum as well as Social minimum baskets based on average prices of 2019. Both indicators are important for assessing the well-being of households. Subsistence minimum defines the lowest possible level of consumption allowing the households to survive, while Social minimum defines a model category allowing the minimum level of decent life, necessary for social integration. Between these two extremes there is a sphere of scarcity. In 2019, the minimum subsistence rate in a one-person household increased by 4.3% and the minimum subsistence rate by 3.8%, with the inflation rate of 2.3%. Under these conditions, various poverty indicators in Poland have decreased compared to 2018.

Homotopy Invariance of Convolution Products

The purpose of this paper is to show that various convolution products are fully homotopical, meaning that they preserve weak equivalences in both variables without any cofibrancy hypothesis. We establish this property for diagrams of simplicial sets indexed by the category of finite sets and injections and for tame $M$-simplicial sets, with $M$ the monoid of injective self-maps of the positive natural numbers. We also show that a certain convolution product studied by Nikolaus and the 1st author is fully homotopical. This implies that every presentably symmetric monoidal $\infty $-category can be represented by a symmetric monoidal model category with a fully homotopical monoidal product.