Examples
- If C has products, then given an isomorphism the mapping, composed with the canonical map of symmetry, is a partial involution.
- If C is a triangulated category, the Karoubi envelope Split(C) can be endowed with the structure of a triangulated category such that the canonical functor C → Split(C) becomes a triangulated functor.
- The Karoubi envelope is used in the construction of several categories of motives.
- The Karoubi envelope construction takes semi-adjunctions to adjunctions. For this reason the Karoubi envelope is used in the study of models of the untyped lambda calculus. The Karoubi envelope of an extensional lambda model (a monoid, considered as a category) is cartesian closed.
Read more about this topic: Karoubi Envelope
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)