From a geometrical point of view: a study of the history and philosophy of category theory
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Dordrecht [u.a.]
Springer
2009
|
Schriftenreihe: | Logic, epistemology, and the unity of science
14 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | X, 309 S. graph. Darst. |
ISBN: | 9781402093838 |
Internformat
MARC
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100 | 1 | |a Marquis, Jean-Pierre |e Verfasser |4 aut | |
245 | 1 | 0 | |a From a geometrical point of view |b a study of the history and philosophy of category theory |c by Jean-Pierre Marquis |
264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2009 | |
300 | |a X, 309 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Logic, epistemology, and the unity of science |v 14 | |
648 | 7 | |a Geschichte |2 gnd |9 rswk-swf | |
650 | 4 | |a Catégories (Mathématiques) - Histoire | |
650 | 4 | |a Catégories (Mathématiques) - Philosophie | |
650 | 7 | |a Catégories (mathématiques) - Histoire |2 ram | |
650 | 7 | |a Catégories (mathématiques) - Philosophie |2 ram | |
650 | 4 | |a Geschichte | |
650 | 4 | |a Philosophie | |
650 | 4 | |a Categories (Mathematics) |x History | |
650 | 4 | |a Categories (Mathematics) |x Philosophy | |
650 | 0 | 7 | |a Kategorientheorie |0 (DE-588)4120552-2 |2 gnd |9 rswk-swf |
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689 | 0 | 1 | |a Geschichte |A z |
689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
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---|---|
adam_text | CONTENTS INTRODUCTION . 1 CATEGORY THEORY AND KLEIN S ERLANGEN PROGRAM 9
1.1 EILENBERG AND MAC LANE S CLAIM. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 9 1.2 KLEIN S PROGRAM: BASIC
ASPECTS............................... 12 1.2.1 A PHILOSOPHICAL FABLE 12
1.2.2 TRANSFORMATION GROUPS: ENCODING BASIC GEOMETRIE FACTS .. 15 1.2.3
TRANSFER OF STRUCTURE: THE IRRELEVANCE OF THE NATURE OF THE ELEMENTS OF
ASPACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
25 1.2.4 WHY A TRANSFORMATION GROUP IS NOT QUITE ENOUGH 28 1.2.5 BUT
THEN AGAIN, WHY A GROUP IS ENOUGH 29 1.2.6 CLASSIFYING GEOMETRIES . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .. 31 1.3 LOGICAL
REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . .. 32 1.4 MAIN ONTOLOGICAL AND EPISTEMOLOGICAL
CONSEQUENCES OF KLEIN S PROGRAM 34 1.5 GROUPS AND GEOMETRIES: FORMAL
SUPERVENIENCE AND REDUCTION 36 1.6 SUMMING UP . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .. 39 2 INTRODUCING CATEGORIES, FUNCTORS
AND NATURAL TRANSFORMATIONS . . . .. 41 2.1 FROM A TRANSFORMATION GROUP
TO THE ALGEBRA OF MAPPINGS . . . . . . .. 44 2.2 FOUNDATIONS OF CATEGORY
THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51 2.3
PHILOSOPHICAL INTERLUDE: AN ARGUMENT AGAINST THE FOUNDATIONAL STATUS OF
CATEGORY THEORY .... . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . .. 54 2.4 AT LAST, NATURAL TRANSFORMATIONS 60 2.5 EXTENDING
KLEIN S PROGRAM IN THE WRONG DIRECTION 64 2.6 CATEGORY THEORY: THE FIRST
PHASE 1945-1958 67 3 CATEGORIES AS SPACES, FUNCTORS AS TRANSFORMATIONS
73 3.1 UNIVERSAL MORPHISMS ... . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .. 74 3.1.1 MAC LANE: DOING DUALITY WITHOUT
ELEMENTS. . . . . . . . . . . . .. 77 3.1.2 UNIVERSAL MORPHISMS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86 IX X
CONTENTS 3.2 GROTHENDIECK AND ABELIAN CATEGORIES 90 3.2.1 ABELIAN
CATEGORIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .. 92 3.2.2 REPRESENTABLE FUNCTORS 102 4 DISEOVERING FUNDAMENTAL
CATEGORICAL TRANSFORMATIONS: ADJOINT FUNETORS 109 4.1 THE BACKGROUND:
HOMOTOPY THEORY AND CATEGORY THEORY 114 4.2 KAN S DISCOVERY 125 4.3 KAN
S 1958 PAPERS ADJOINT FUNETORS 132 5 ADJOINT FUNETORS: WHAT THEY ARE,
WHAT THEY MEAN 147 5.1 ADJOINTNESS 148 5.2 EQUIVALENEE OF CATEGORIES
AGAIN 161 5.3 BACK TO KLEIN 164 5.4 FROM GROUPS TO GROUPOIDS 166 5.5 THE
FOUNDATIONS OF CATEGORY THEORY AGAIN 175 6 INVARIANTS IN FOUNDATIONS:
AIGEBRAIE LOGIE 191 6.1 LAWVERE S THESIS 194 6.2 THE CATEGORY OF
CATEGORIES AS A FOUNDATIONAL FRAMEWORK 197 6.3 THE ELEMENTARY THEORY OF
THE CATEGORY OF SETS 208 6.4 CATEGORIEAL LOGIE: THE PROGRAM 210 6.5 AN
ADJOINT PRESENTATION OF PROPOSITIONAL LOGIE 216 6.6 QUANTIFIERS AS
ADJOINT FUNETORS 220 6.7 GRAPHIEAL SYNTAX: SKETCHES 225 6.8 CATEGORIEAL
THEORIES: CONEEPTUAL AND GENERIE STRUCTURES 234 6.9 SUMMING UP 246 7
INVARIANTS IN FOUNDATIONS: GEOMETRIE LOGIE 247 7.1 GROTHENDIEEK TOPOSES:
GENERALIZED SPAEES 248 7.2 ELEMENTARY TOPOSES 261 7.3 INVARIANTS UNDER
GEOMETRIE TRANSFORMATIONS 267 7.4 INVARIANTS UNDER LOGIEAL
TRANSFORMATIONS 271 7.5 INVARIANT FOUNDATIONAL FRAMEWORKS 276 7.6 USING
GEOMETRIE AND LOGIEAL INVARIANTS 282 7.7 SUMMING UP 283 CONCLUSION 285
REFERENEES 291 INDEX 303
|
adam_txt |
CONTENTS INTRODUCTION . 1 CATEGORY THEORY AND KLEIN'S ERLANGEN PROGRAM 9
1.1 EILENBERG AND MAC LANE'S CLAIM. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 9 1.2 KLEIN'S PROGRAM: BASIC
ASPECTS. 12 1.2.1 A PHILOSOPHICAL FABLE 12
1.2.2 TRANSFORMATION GROUPS: ENCODING BASIC GEOMETRIE FACTS . 15 1.2.3
TRANSFER OF STRUCTURE: THE IRRELEVANCE OF THE NATURE OF THE ELEMENTS OF
ASPACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25 1.2.4 WHY A TRANSFORMATION GROUP IS NOT QUITE ENOUGH 28 1.2.5 BUT
THEN AGAIN, WHY A GROUP IS ENOUGH 29 1.2.6 CLASSIFYING GEOMETRIES . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.3 LOGICAL
REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 32 1.4 MAIN ONTOLOGICAL AND EPISTEMOLOGICAL
CONSEQUENCES OF KLEIN 'S PROGRAM 34 1.5 GROUPS AND GEOMETRIES: FORMAL
SUPERVENIENCE AND REDUCTION 36 1.6 SUMMING UP . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 39 2 INTRODUCING CATEGORIES, FUNCTORS
AND NATURAL TRANSFORMATIONS . . . . 41 2.1 FROM A TRANSFORMATION GROUP
TO THE ALGEBRA OF MAPPINGS . . . . . . . 44 2.2 FOUNDATIONS OF CATEGORY
THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.3
PHILOSOPHICAL INTERLUDE: AN ARGUMENT AGAINST THE FOUNDATIONAL STATUS OF
CATEGORY THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 54 2.4 AT LAST, NATURAL TRANSFORMATIONS 60 2.5 EXTENDING
KLEIN'S PROGRAM IN THE WRONG DIRECTION 64 2.6 CATEGORY THEORY: THE FIRST
PHASE 1945-1958 67 3 CATEGORIES AS SPACES, FUNCTORS AS TRANSFORMATIONS
73 3.1 UNIVERSAL MORPHISMS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 74 3.1.1 MAC LANE: DOING DUALITY WITHOUT
ELEMENTS. . . . . . . . . . . . . 77 3.1.2 UNIVERSAL MORPHISMS . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 IX X
CONTENTS 3.2 GROTHENDIECK AND ABELIAN CATEGORIES 90 3.2.1 ABELIAN
CATEGORIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 92 3.2.2 REPRESENTABLE FUNCTORS 102 4 DISEOVERING FUNDAMENTAL
CATEGORICAL TRANSFORMATIONS: ADJOINT FUNETORS 109 4.1 THE BACKGROUND:
HOMOTOPY THEORY AND CATEGORY THEORY 114 4.2 KAN'S DISCOVERY 125 4.3 KAN
'S 1958 PAPERS "ADJOINT FUNETORS" 132 5 ADJOINT FUNETORS: WHAT THEY ARE,
WHAT THEY MEAN 147 5.1 ADJOINTNESS 148 5.2 EQUIVALENEE OF CATEGORIES
AGAIN 161 5.3 BACK TO KLEIN 164 5.4 FROM GROUPS TO GROUPOIDS 166 5.5 THE
FOUNDATIONS OF CATEGORY THEORY AGAIN 175 6 INVARIANTS IN FOUNDATIONS:
AIGEBRAIE LOGIE 191 6.1 LAWVERE'S THESIS 194 6.2 THE CATEGORY OF
CATEGORIES AS A FOUNDATIONAL FRAMEWORK 197 6.3 THE ELEMENTARY THEORY OF
THE CATEGORY OF SETS 208 6.4 CATEGORIEAL LOGIE: THE PROGRAM 210 6.5 AN
ADJOINT PRESENTATION OF PROPOSITIONAL LOGIE 216 6.6 QUANTIFIERS AS
ADJOINT FUNETORS 220 6.7 GRAPHIEAL SYNTAX: SKETCHES 225 6.8 CATEGORIEAL
THEORIES: CONEEPTUAL AND GENERIE STRUCTURES 234 6.9 SUMMING UP 246 7
INVARIANTS IN FOUNDATIONS: GEOMETRIE LOGIE 247 7.1 GROTHENDIEEK TOPOSES:
GENERALIZED SPAEES 248 7.2 ELEMENTARY TOPOSES 261 7.3 INVARIANTS UNDER
GEOMETRIE TRANSFORMATIONS 267 7.4 INVARIANTS UNDER LOGIEAL
TRANSFORMATIONS 271 7.5 INVARIANT FOUNDATIONAL FRAMEWORKS 276 7.6 USING
GEOMETRIE AND LOGIEAL INVARIANTS 282 7.7 SUMMING UP 283 CONCLUSION 285
REFERENEES 291 INDEX 303 |
any_adam_object | 1 |
any_adam_object_boolean | 1 |
author | Marquis, Jean-Pierre |
author_facet | Marquis, Jean-Pierre |
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author_sort | Marquis, Jean-Pierre |
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callnumber-label | QA169 |
callnumber-raw | QA169 |
callnumber-search | QA169 |
callnumber-sort | QA 3169 |
callnumber-subject | QA - Mathematics |
classification_rvk | CC 2600 SG 580 |
ctrlnum | (OCoLC)495359320 (DE-599)BVBBV035155209 |
dewey-full | 512.6209 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512.6209 |
dewey-search | 512.6209 |
dewey-sort | 3512.6209 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik Philosophie |
discipline_str_mv | Mathematik Philosophie |
era | Geschichte gnd |
era_facet | Geschichte |
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id | DE-604.BV035155209 |
illustrated | Illustrated |
index_date | 2024-07-02T22:48:21Z |
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institution | BVB |
isbn | 9781402093838 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016962401 |
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physical | X, 309 S. graph. Darst. |
publishDate | 2009 |
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series | Logic, epistemology, and the unity of science |
series2 | Logic, epistemology, and the unity of science |
spelling | Marquis, Jean-Pierre Verfasser aut From a geometrical point of view a study of the history and philosophy of category theory by Jean-Pierre Marquis Dordrecht [u.a.] Springer 2009 X, 309 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Logic, epistemology, and the unity of science 14 Geschichte gnd rswk-swf Catégories (Mathématiques) - Histoire Catégories (Mathématiques) - Philosophie Catégories (mathématiques) - Histoire ram Catégories (mathématiques) - Philosophie ram Geschichte Philosophie Categories (Mathematics) History Categories (Mathematics) Philosophy Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Geschichte z DE-604 Logic, epistemology, and the unity of science 14 (DE-604)BV019709027 14 Digitalisierung UB Erlangen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016962401&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Marquis, Jean-Pierre From a geometrical point of view a study of the history and philosophy of category theory Logic, epistemology, and the unity of science Catégories (Mathématiques) - Histoire Catégories (Mathématiques) - Philosophie Catégories (mathématiques) - Histoire ram Catégories (mathématiques) - Philosophie ram Geschichte Philosophie Categories (Mathematics) History Categories (Mathematics) Philosophy Kategorientheorie (DE-588)4120552-2 gnd |
subject_GND | (DE-588)4120552-2 |
title | From a geometrical point of view a study of the history and philosophy of category theory |
title_auth | From a geometrical point of view a study of the history and philosophy of category theory |
title_exact_search | From a geometrical point of view a study of the history and philosophy of category theory |
title_exact_search_txtP | From a geometrical point of view a study of the history and philosophy of category theory |
title_full | From a geometrical point of view a study of the history and philosophy of category theory by Jean-Pierre Marquis |
title_fullStr | From a geometrical point of view a study of the history and philosophy of category theory by Jean-Pierre Marquis |
title_full_unstemmed | From a geometrical point of view a study of the history and philosophy of category theory by Jean-Pierre Marquis |
title_short | From a geometrical point of view |
title_sort | from a geometrical point of view a study of the history and philosophy of category theory |
title_sub | a study of the history and philosophy of category theory |
topic | Catégories (Mathématiques) - Histoire Catégories (Mathématiques) - Philosophie Catégories (mathématiques) - Histoire ram Catégories (mathématiques) - Philosophie ram Geschichte Philosophie Categories (Mathematics) History Categories (Mathematics) Philosophy Kategorientheorie (DE-588)4120552-2 gnd |
topic_facet | Catégories (Mathématiques) - Histoire Catégories (Mathématiques) - Philosophie Catégories (mathématiques) - Histoire Catégories (mathématiques) - Philosophie Geschichte Philosophie Categories (Mathematics) History Categories (Mathematics) Philosophy Kategorientheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016962401&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV019709027 |
work_keys_str_mv | AT marquisjeanpierre fromageometricalpointofviewastudyofthehistoryandphilosophyofcategorytheory |