Skip to main content
MathOverflow

Return to Question

replaced http://mathoverflow.net/ with https://mathoverflow.net/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

A lot of the terminology of category theory has obvious antecedents in analysis: limits, completeness, adjunctions, continuous (functors), to name but a few. However, analysis and category theory seem to be at opposite poles of the spectrum.

Is there anything deep here, or is it a case of "it has wings, so let's call it a duck"?

This was partly inspired by the top-rated answer to the question What is a metric space?What is a metric space? and by the (slightly unsatisfactory answers to the) question Can adjoint linear transformations be naturally realized as adjoint functors?Can adjoint linear transformations be naturally realized as adjoint functors?. In particular, in the first case - the categorical view of metric spaces - there does seem to be an obvious route between the two worlds, do the terminologies correspond there?

A lot of the terminology of category theory has obvious antecedents in analysis: limits, completeness, adjunctions, continuous (functors), to name but a few. However, analysis and category theory seem to be at opposite poles of the spectrum.

Is there anything deep here, or is it a case of "it has wings, so let's call it a duck"?

This was partly inspired by the top-rated answer to the question What is a metric space? and by the (slightly unsatisfactory answers to the) question Can adjoint linear transformations be naturally realized as adjoint functors?. In particular, in the first case - the categorical view of metric spaces - there does seem to be an obvious route between the two worlds, do the terminologies correspond there?

A lot of the terminology of category theory has obvious antecedents in analysis: limits, completeness, adjunctions, continuous (functors), to name but a few. However, analysis and category theory seem to be at opposite poles of the spectrum.

Is there anything deep here, or is it a case of "it has wings, so let's call it a duck"?

This was partly inspired by the top-rated answer to the question What is a metric space? and by the (slightly unsatisfactory answers to the) question Can adjoint linear transformations be naturally realized as adjoint functors?. In particular, in the first case - the categorical view of metric spaces - there does seem to be an obvious route between the two worlds, do the terminologies correspond there?

Source Link
Andrew Stacey
Andrew Stacey
  • 26.8k
  • 12
  • 113
  • 187

Terminology in category theory

A lot of the terminology of category theory has obvious antecedents in analysis: limits, completeness, adjunctions, continuous (functors), to name but a few. However, analysis and category theory seem to be at opposite poles of the spectrum.

Is there anything deep here, or is it a case of "it has wings, so let's call it a duck"?

This was partly inspired by the top-rated answer to the question What is a metric space? and by the (slightly unsatisfactory answers to the) question Can adjoint linear transformations be naturally realized as adjoint functors?. In particular, in the first case - the categorical view of metric spaces - there does seem to be an obvious route between the two worlds, do the terminologies correspond there?