Summary
The topos concept arose in algebraic geometry, as a consequence of combining the concept of sheaf and closure under categorical operations. It plays a certain definite role in cohomology theories.
The subsequent developments associated with logic are more interdisciplinary. They include examples drawing on homotopy theory (classifying toposes). They involve links between category theory and mathematical logic, and also (as a high-level, organisational discussion) between category theory and theoretical computer science based on type theory. Granted the general view of Saunders Mac Lane about ubiquity of concepts, this gives them a definite status. A 'killer application' is étale cohomology.
Read more about this topic: History Of Topos Theory
Famous quotes containing the word summary:
“Product of a myriad various minds and contending tongues, compact of obscure and minute association, a language has its own abundant and often recondite laws, in the habitual and summary recognition of which scholarship consists.”
—Walter Pater (1839–1894)
“I have simplified my politics into an utter detestation of all existing governments; and, as it is the shortest and most agreeable and summary feeling imaginable, the first moment of an universal republic would convert me into an advocate for single and uncontradicted despotism. The fact is, riches are power, and poverty is slavery all over the earth, and one sort of establishment is no better, nor worse, for a people than another.”
—George Gordon Noel Byron (1788–1824)