Captain and Chief officer are overlapping terms, formal or informal, for the commander of a military unit, the commander of a ship, airplane, spacecraft, or other vessel, or the commander of a port, fire department or police department, election precinct, etc. Captain is a military rank in armies, navies, coast guards, etc., typically at the level of an officer commanding a company of infantry, a ship, or a battery of artillery, or similar distinct unit. Chief officer may be used interchangeably with captain in some situations, as when a Captain-ranked Navy officer is serving as the commander of a ship. The terms also may be used as an informal or honorary title for persons in similar commanding roles. In mining (esp. Cornish), it is an honorific given the superintendent or manager of a mine.
The term "captain" derives from katepánō (Greek: κατεπάνω, lit. "[the one] placed at the top", or " the topmost") which was used as title for a senior Byzantine military rank and office. The word was Latinized as capetanus/catepan, and its meaning seems to have merged with that of the Italian "capitaneus" (which derives from the Latin word "caput", meaning head). This hybridized term gave rise to the English language term captain and its equivalents in other languages (Capitan, Kapitan, Kapitän, El Capitan, Il Capitano, Kapudan Pasha etc.)
CAPT may refer to:
Product may refer to:
In linear algebra:
In abstract algebra:
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.
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.
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 (Xi)i∈I of objects iff there exist morphisms πi : X → Xi, such that for every object Y and a I-indexed family of morphisms fi : Y → Xi there exists a unique morphism f : Y → X such that the following diagrams commute for all i∈I: