Product

Product may refer to:

Business

Sciences

Mathematics

In linear algebra:

In abstract algebra:

Product breakdown structure

In project management, a product breakdown structure (PBS) is a tool for analysing, documenting and communicating the outcomes of a project, and forms part of the product based planning technique.

The PBS provides ''an exhaustive, hierarchical tree structure of deliverables (physical, functional or conceptual) that make up the project, arranged in whole-part relationship'' (Duncan, 2015).

This diagrammatic representation of project outputs provides a clear and unambiguous statement of what the project is to deliver.

The PBS is identical in format to the work breakdown structure (WBS), but is a separate entity and is used at a different step in the planning process. The PBS precedes the WBS and focuses on cataloguing all the desired outputs (products) needed to achieve the goal of the project. This feeds into creation of the WBS, which identifies the tasks and activities required to deliver those outputs. Supporters of product based planning suggest that this overcomes difficulties that arise from assumptions about what to do and how to do it by focusing instead on the goals and objectives of the project - an oft-quoted analogy is that PBS defines where you want to go, the WBS tells you how to get there.

Product (category theory)

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.

Definition

Let C be a category with some objects X₁ and X₂. An object X is a product of X₁ and X₂, denoted X₁ × X₂, if it satisfies this universal property:

The unique morphism f is called the product of morphisms f₁ and f₂ and is denoted < f₁, f₂ >. The morphisms π₁ and π₂ are called the canonical projections or projection morphisms.

Above we defined the binary product. Instead of two objects we can take an arbitrary family of objects indexed by some set I. Then we obtain the definition of a product.

An object X is the product of a family (X_i)_i∈I of objects iff there exist morphisms π_i : X → X_i, such that for every object Y and a I-indexed family of morphisms f_i : Y → X_i there exists a unique morphism f : Y → X such that the following diagrams commute for all i∈I:

Sect

A sect is a subgroup of a religious, political or philosophical belief system, usually an offshoot of a larger religious group. Although in past it was mostly used to refer to religious groups, it has since expanded and in modern culture can refer to any organization that breaks away from a larger one to follow a different set of rules and principles. The term is occasionally used in a malicious way to suggest the broken-off group follows a more negative path than the original. The historical usage of the term sect in Christendom has had pejorative connotations, referring to a group or movement with heretical beliefs or practices that deviate from those of groups considered orthodox.

A sect as used in an Indian context refers to an organized tradition.

Etymology

The word sect comes from the Latin noun secta (a feminine form of a variant past participle of the verb sequi, to follow), meaning "a way, road", and figuratively a (prescribed) way, mode, or manner, and hence metonymously, a discipline or school of thought as defined by a set of methods and doctrines. The present gamut of meanings of sect has been influenced by confusion with the homonymous (but etymologically unrelated) Latin word secta (the feminine form of the past participle of the verb secare, to cut), as though sects were scissions cast aside from the mainstream religion.

Planescape

Planescape is a campaign setting for the Dungeons & Dragons fantasy role-playing game, originally designed by Zeb Cook. The Planescape setting was published in 1994. As its name suggests, the setting crosses and comprises the numerous planes of existence, encompassing an entire cosmology called the Great Wheel, as originally developed in the Manual of the Planes by Jeff Grubb. This includes many of the other Dungeons & Dragons worlds, linking them via inter-dimensional magical portals.

Development

Planescape is an expansion of ideas presented in the Advanced Dungeons & Dragons Dungeon Master's Guide (First Edition) and the original Manual of the Planes. When Advanced Dungeons & Dragons 2nd edition was published, a decision was made not to include angelic or demonic creatures, and so the cosmology was largely ignored, being replaced (to a certain degree) by the Spelljammer setting. However, fan demand for a 2nd Edition Manual of the Planes was strong enough to justify its expansion into a full-fledged campaign setting, and so in 1994 Planescape was released.

Sect (World of Darkness)

In the role-playing games and books based on the World of Darkness setting, by White Wolf Game Studio, a sect is a large organization of vampires with a leadership, rules and goals, that (at least in theory) trascend clan divisions.

In the modern setting (e.g. Vampire: The Masquerade) there are two main sects, the Camarilla and the Sabbat. Each clan is typically associated with a sect, but in many cases a minor group of members of a clan are associated with the other (these are called antitribu).

Among the minor subgroups of vampires there are the Anarchs, along with others that call themselves independent. The following clans have no sect allegiances, but some consider them whole sects unto themselves: Assamite, Followers of Set, Giovanni and Ravnos. Additionally, many bloodlines are not affiliated with either sect.

Vampire: The Requiem

In the new World of Darkness games, specifically the replacement for Vampire: The Masquerade called Vampire: The Requiem, the sects are replaced by numerous smaller organisations called "covenants".