1:29:52Lecture 02: Universal Constructions, Limits and Colimits
A 90-minute video from Mathematical Structuralism: “Lecture 02: Universal Constructions, Limits and Colimits”.
Mathematical Structuralism
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1:29:52
1:31:37Lecture 03: Interpretation of a Fragment of First-order Language
A 92-minute video from Mathematical Structuralism: “Lecture 03: Interpretation of a Fragment of First-order Language”.
1:39:53Lecture 04: Elementary Toposes
A 100-minute video from Mathematical Structuralism: “Lecture 04: Elementary Toposes”.
1:39:28Lecture 05: Functors and Natural Transformations
A 99-minute video from Mathematical Structuralism: “Lecture 05: Functors and Natural Transformations”.
1:29:55Lecture 06: Topos of Variable Sets
A 90-minute video from Mathematical Structuralism: “Lecture 06: Topos of Variable Sets”.
1:30:44Lecture 07: Presheaves as Generalized Spaces
A 91-minute video from Mathematical Structuralism: “Lecture 07: Presheaves as Generalized Spaces”.
1:32:07Lecture 08.5: Examples of the Categories of Presheaves
A 92-minute video from Mathematical Structuralism: “Lecture 08.5: Examples of the Categories of Presheaves”.
1:27:21Lecture 08: Yoneda Lemma and Free Cocompletion
A 87-minute video from Mathematical Structuralism: “Lecture 08: Yoneda Lemma and Free Cocompletion”.
1:36:49Lecture 09: Coverages and Sheaves I
A 97-minute video from Mathematical Structuralism: “Lecture 09: Coverages and Sheaves I”.
1:42:05Lecture 10: Coverages and Sheaves II
A 102-minute video from Mathematical Structuralism: “Lecture 10: Coverages and Sheaves II”.
1:28:10Lecture 11: The Need for Sheaves
A 88-minute video from Mathematical Structuralism: “Lecture 11: The Need for Sheaves”.
1:45:26Lecture 12: Grothendieck Toposes
A 105-minute video from Mathematical Structuralism: “Lecture 12: Grothendieck Toposes”.
1:37:24Lecture 13: Overview of Previous Lectures
A 97-minute video from Mathematical Structuralism: “Lecture 13: Overview of Previous Lectures”.
1:40:49Lecture 14: Heyting-valued Sets I
A 101-minute video from Mathematical Structuralism: “Lecture 14: Heyting-valued Sets I”.
1:39:44Lecture 15: Heyting-valued Sets II
A 100-minute video from Mathematical Structuralism: “Lecture 15: Heyting-valued Sets II”.
1:43:21Lecture 16: Interpretation of the Full First-order Language
A 103-minute video from Mathematical Structuralism: “Lecture 16: Interpretation of the Full First-order Language”.
1:31:47Lecture 17: Independence of the Continuum Hypothesis and Pigeonhole Principle
A 92-minute video from Mathematical Structuralism: “Lecture 17: Independence of the Continuum Hypothesis and Pigeonhole Principle”.
1:40:29Lecture 18: Realizability
A 100-minute video from Mathematical Structuralism: “Lecture 18: Realizability”.
1:46:57Lecture 19: The Effective Topos
A 107-minute video from Mathematical Structuralism: “Lecture 19: The Effective Topos”.
55:53Lecture 22, Part 1: Profinite sets, Profinite groups and some philosophical notes on structuralsim
A 56-minute video from Mathematical Structuralism: “Lecture 22, Part 1: Profinite sets, Profinite groups and some philosophical notes on structuralsim”.
1:26:37Lecture 22, Part 2: Profinite sets, Profinite groups and some philosophical notes on structuralsim
A 87-minute video from Mathematical Structuralism: “Lecture 22, Part 2: Profinite sets, Profinite groups and some philosophical notes on structuralsim”.
55:04Lecture 23, Part 1: Flat modules, functoriality of (co)limits and (co)limit-preserving functors
A 55-minute video from Mathematical Structuralism: “Lecture 23, Part 1: Flat modules, functoriality of (co)limits and (co)limit-preserving functors”.
1:20:21Lecture 23, Part 2: Flat modules, functoriality of (co)limits and (co)limit-preserving functors
A 80-minute video from Mathematical Structuralism: “Lecture 23, Part 2: Flat modules, functoriality of (co)limits and (co)limit-preserving functors”.
1:05:20Lecture 24, Part 1: (Co)limits in Functor Categories and Non-(co)limit preserving Functors
A 65-minute video from Mathematical Structuralism: “Lecture 24, Part 1: (Co)limits in Functor Categories and Non-(co)limit preserving Functors”.
56:18Lecture 24, Part 2: (Co)limits in Functor Categories and Non-(co)limit preserving Functors
A 56-minute video from Mathematical Structuralism: “Lecture 24, Part 2: (Co)limits in Functor Categories and Non-(co)limit preserving Functors”.
55:44Lecture 25, Part 1: van Kampen theorem and limit preservation of representables
A 56-minute video from Mathematical Structuralism: “Lecture 25, Part 1: van Kampen theorem and limit preservation of representables”.
50:57Lecture 25, Part 2: van Kampen theorem and limit preservation of representables
A 51-minute video from Mathematical Structuralism: “Lecture 25, Part 2: van Kampen theorem and limit preservation of representables”.
1:25:01Lecture 26, Part 1: "Projective" line, its non-representability and reflected (co)limits
A 85-minute video from Mathematical Structuralism: “Lecture 26, Part 1: "Projective" line, its non-representability and reflected (co)limits”.
35:32Lecture 26, Part 2: "Projective" line, its non-representability and reflected (co)limits
A 36-minute video from Mathematical Structuralism: “Lecture 26, Part 2: "Projective" line, its non-representability and reflected (co)limits”.
1:32:54Lecture 27, Part 1: (Co)Limit creation, commutation of (co)limits and some philosophical discussions
A 93-minute video from Mathematical Structuralism: “Lecture 27, Part 1: (Co)Limit creation, commutation of (co)limits and some philosophical discussions”.
45:47Lecture 27, Part 2: (Co)Limit creation, commutation of (co)limits and some philosophical discussions
A 46-minute video from Mathematical Structuralism: “Lecture 27, Part 2: (Co)Limit creation, commutation of (co)limits and some philosophical discussions”.
1:24:38Lecture 28, Part 1: Possible commutations of limits and colimts and some philosophical discussions
A 85-minute video from Mathematical Structuralism: “Lecture 28, Part 1: Possible commutations of limits and colimts and some philosophical discussions”.
1:13:06Lecture 28, Part 2: Possible commutations of limits and colimts and some philosophical discussions
A 73-minute video from Mathematical Structuralism: “Lecture 28, Part 2: Possible commutations of limits and colimts and some philosophical discussions”.
1:23:50Lecture 29, Part 1: Finite limits and filtered colimits and the category of elements
A 84-minute video from Mathematical Structuralism: “Lecture 29, Part 1: Finite limits and filtered colimits and the category of elements”.
57:48Lecture 29, Part 2: Finite limits and filtered colimits and the category of elements
A 58-minute video from Mathematical Structuralism: “Lecture 29, Part 2: Finite limits and filtered colimits and the category of elements”.
53:55Lecture 30, Part 1: Category of elements and some philosophical discussions
A 54-minute video from Mathematical Structuralism: “Lecture 30, Part 1: Category of elements and some philosophical discussions”.