In category theory, the concept of an **end** is a particular construction that arises when dealing with functors from one category to another. Specifically, an end is a way to "sum up" or "integrate" the values of a functor over a category, similar to how an integral works in calculus but in a categorical context.
Ind-completion is a concept from the field of category theory, specifically related to the completion of a category with respect to a certain type of structure or property. In mathematical contexts, "ind-completion" often refers to a way of completing a category by formally adding certain limits or colimits.
In mathematics, particularly in the field of representation theory and algebra, a **Schur functor** is an important concept that arises in the context of polynomial functors. Schur functors are used to construct representations of symmetric groups and to study tensors, modules, and various other algebraic structures.
In category theory, a **subfunctor** is a concept that extends the idea of a subobject to the context of functors. While subobjects represent "parts" of objects in a category, subfunctors represent "parts" of functors in a more structured manner. ### Definition Let \( F: \mathcal{C} \to \mathcal{D} \) be a functor.
A string diagram is a visual representation used in various fields, most prominently in mathematics and physics, particularly in category theory and string theory. The term may be interpreted in different contexts, but here are the two primary uses: 1. **String Diagrams in Category Theory**: - In category theory, string diagrams are a way to visualize morphisms (arrows) and objects (points) within a category.
In category theory, a coproduct is a generalization of the concept of a disjoint union of sets, and more broadly, it can be thought of as a way to combine objects in a category. The coproduct of a collection of objects provides a means of "merging" these objects while preserving their individual identities.
In category theory, a **product** is a fundamental construction that generalizes the notion of the Cartesian product from set theory to arbitrary categories. The concept of a product allows us to describe the way in which objects and morphisms (arrows) can be combined in a categorical context.
The Monster group, denoted as \( \mathbb{M} \) or sometimes \( \text{Mon} \), is the largest of the 26 sporadic simple groups in group theory, a branch of mathematics that studies algebraic structures known as groups. It was first discovered by Robert Griess in 1982 and has a rich structure that connects various areas of mathematics, including number theory, geometry, and mathematical physics.
A *free-by-cyclic group* is a specific type of group that can be thought of as a combination of two structures: a free group and a cyclic group. More formally, a free-by-cyclic group is a group \( G \) that can be expressed in the form: \[ G = F \rtimes C \] where \( F \) is a free group and \( C \) is a cyclic group.
In group theory, a branch of abstract algebra, an **infinite group** is a group that contains an infinite number of elements. In other words, if the cardinality (size) of the group is not a finite number, then the group is classified as infinite. Infinite groups can be categorized into various types based on their structure and properties.
Melaleuca, Inc. v. Hansen is a legal case that involved issues surrounding contract law, specifically concerning non-compete agreements and business practices. Melaleuca, Inc. is a large company that sells various health and wellness products, and it has been involved in litigation regarding its distributors and the terms of their agreements.
Google bombing is a technique used to manipulate search engine results in order to make a particular website or page appear higher in search rankings for specific keywords or phrases, usually through the strategic use of backlinks and anchor text. This often involves a group of people linking to a particular site using the same phrase, in an effort to associate that phrase with the website in Google's algorithms. One of the most famous examples of Google bombing occurred in the mid-2000s when users linked to the George W.
The Mpemba effect is an observed phenomenon where hot water can freeze faster than cold water under certain conditions. Named after Tanzanian student Erasto Mpemba, who noticed this effect in the 1960s, the effect has intrigued scientists and led to various hypotheses explaining why it occurs.
The Preisach model of hysteresis is a mathematical representation used to describe and analyze the hysteretic behavior of materials and systems. It is particularly relevant in the study of ferromagnetic and ferroelectric materials, where the relationship between external inputs (like magnetic or electric fields) and outputs (like magnetization or polarization) exhibits a non-linear behavior that depends on the history of the applied field.
Wetting refers to the ability of a liquid to maintain contact with a solid surface, resulting from adhesive forces between the liquid and the solid. This phenomenon is particularly important in various fields such as chemistry, materials science, and biology. When a liquid is poured onto a solid surface, the extent to which the liquid spreads out or forms droplets depends on the balance between cohesive forces (the forces holding the liquid molecules together) and adhesive forces (the forces between the liquid molecules and the surface).
Dynamic insulation is a concept that involves a building envelope designed to adapt to varying environmental conditions, aiming to optimize thermal performance while using less energy. Unlike traditional insulation methods that provide a static barrier to heat transfer, dynamic insulation systems actively respond to changes in temperature and humidity. Key features of dynamic insulation can include: 1. **Responsive Materials**: These materials can change their thermal properties based on external conditions, such as temperature and moisture levels.
Relative volatility is a measure used in the field of chemical engineering, particularly in distillation and separation processes, to quantify the ease with which one component in a mixture can be separated from another component. It is defined as the ratio of the vapor pressures of two components in a liquid mixture.
Storm Barra was a significant weather event that affected parts of Europe in December 2021. It was classified as a named storm by the UK Met Office and brought heavy rain, strong winds, and severe weather conditions to various regions, particularly in the UK and Ireland. The storm led to widespread disruption, including power outages, travel disruptions, and property damage due to high winds and flooding.
The heat equation is a fundamental partial differential equation that describes how the distribution of heat (or temperature) in a given region evolves over time. It is a mathematical model used in various fields such as physics, engineering, and finance to study heat conduction, diffusion, and other related processes.
The heat transfer coefficient is a measure of the ability of a material or surface to transfer heat between two fluids or between a fluid and a solid surface. It quantifies the rate of heat transfer per unit area per unit temperature difference between the two entities in contact.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact