Categories of modules, comodules and contramodules over representations

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical framework which incorporates all the adjoint functors between these categories in a natural manner. Various classical properties of coalgebras and their morphisms arise naturally within this theory. We also consider cartesian objects in each of these categories, which may be viewed as counterparts of quasi-coherent sheaves over a scheme. We study their categorical properties using cardinality arguments. Our focus is on generators for these categories and on Grothendieck categories, because the latter may be treated as replacements for noncommutative spaces.Comment: Several update

A Gabber type result for representations in Eilenberg-Moore categories

We consider a representation $\mathscr U:\mathbb Q\longrightarrow Mnd(\mathcal C)$ of a quiver $\mathbb Q$ taking values in monads over a Grothendieck category $\mathcal C$. By using adjoint functors between Eilenberg-Moore categories, we consider two different kinds of modules over $\mathscr U$. The first is the category $Mod-\mathscr U$ of $\mathscr U$-modules, which behaves like the category of modules over a ringed space. The second is the category $Cart-\mathscr U$ of cartesian modules, which behave like quasi-coherent sheaves. We give conditions for $Mod-\mathscr U$ and $Cart-\mathscr U$ to be Grothendieck categories. One of our key steps is finding a modulus like bound for an endofunctor $U:\mathcal C\longrightarrow \mathcal C$ in terms of $\kappa(G)$, where $G$ is a generator for $\mathcal C$ and $\kappa(G)$ is a cardinal such that $G$ is $\kappa(G)$-presentable. We conclude with an extension of the classical quasi-coherator construction to modules over a monad quiver with values in Eilenberg-Moore categories

India’s missing working women: Tracing the journey of women’s economic contribution over the last seven decades, and during COVID-19

India today is an economic powerhouse on the global stage. However, it faces a queer conundrum. Despite considerable gains in female education, decreases in fertility rates and increasing economic growth, only a fourth of its women are in the labor force, amongst the lowest in the world. Based on analysis of time series data over the last seven decades (1950-2018), this paper finds that women’s labor force and workforce participation rates have secularly declined to their lowest levels since Independence. Women’s wages have consistently been below men, with weighted average wage gaps increasing from 59% in 1993, to 72% in 2018. The fall in labor force participation has been led by women in rural areas, while female unemployment rates have remained higher than men in urban areas. We find that occupational segregation and concentration of women in low-growth sectors, income effect of rising household earnings, increased mechanization and gender gaps in tertiary education and skill training are leading factors behind the observed labor market outcomes. Recent high-frequency data shows that 15 million women lost their jobs in the first month of the COVID-19 induced lockdown. Even as the overall size of the labor force shrunk by 3% between November 2019 to November 2020, the size of the labor force shrunk by 13% for women, vs. 2% for men. Bringing women back to the workforce requires a differentiated approach, targeting different segments, especially informal workers, microentrepreneurs and the formal sector. Therefore, a diverse mix of targeted policy interventions like gender quotas in public works, easier access to credit for female micro-entrepreneurs, preferential procurement for women-owned business, greater flexibility in workplace arrangements and gender targets for skill training among others would help retain and promote workforce participation for women

Study of Thermodynamic Quantities in Generalized Gravity Theories

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Ho$\check{\text r}$ava-Lifshitz and $f(R)$ gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and $f(R)$ gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Ho$\check{\text r}$ava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Ho$\check{\text r}$ava-Lifshitz gravity.Comment: 15 pages, 12 figure

Multiple roles for basement membrane proteins in cancer progression and EMT

Metastasis or the progression of malignancy poses a major challenge in cancer therapy and is the principal reason for increased mortality. The epithelial-mesenchymal transition (EMT) of the basement membrane (BM) allows cells of epithelial phenotype to transform into a mesenchymal-like (quasi-mesenchymal) phenotype and metastasize via the lymphovascular system through a metastatic cascade by intravasation and extravasation. This helps in the progression of carcinoma from the primary site to distant organs. Collagen, laminin, and integrin are the prime components of BM and help in tumor cell metastasis, which makes them ideal cancer drug targets. Further, recent studies have shown that collagen, laminin, and integrin can be used as a biomarker for metastatic cells. In this review, we have summarized the current knowledge of such therapeutics, which are either currently in preclinical or clinical stages and could be promising cancer therapeutics.Data availability: Not applicableScientific Research at Majmaah University [R-2022-117]Dr. Niraj Kumar Jha is thankful to Sharda University for the infra-structure and facility. The author would like to thank Deanship of Sci-entific Research at Majmaah University for supporting this work under project number No. R-2022-117. The authors would like to acknowledge the support from their respective institutes throughout the review writing process

India’s missing working women: tracing the journey of women’s economic contribution over the last seven decades, and during COVID-19

India today is an economic powerhouse on the global stage. However, it faces a queer conundrum. Despite considerable gains in female education, decreases in fertility rates and increasing economic growth, only a fourth of its women are in the labor force, amongst the lowest in the world. Based on analysis of time series data over the last seven decades (1950-2018), this paper finds that women’s labor force and workforce participation rates have secularly declined to their lowest levels since Independence. Women’s wages have consistently been below men, with weighted average wage gaps increasing from 59% in 1993, to 72% in 2018. The fall in labor force participation has been led by women in rural areas, while female unemployment rates have remained higher than men in urban areas. We find that occupational segregation and concentration of women in low-growth sectors, income effect of rising household earnings, increased mechanization and gender gaps in tertiary education and skill training are leading factors behind the observed labor market outcomes. Recent high-frequency data shows that 15 million women lost their jobs in the first month of the COVID-19 induced lockdown. Even as the overall size of the labor force shrunk by 3% between November 2019 to November 2020, the size of the labor force shrunk by 13% for women, vs. 2% for men. Bringing women back to the workforce requires a differentiated approach, targeting different segments, especially informal workers, microentrepreneurs and the formal sector. Therefore, a diverse mix o