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Corrected spelling of Charles Rezk's surname
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So, here is the key insight that migrates from the modern approach to the post-modern: do not look at a single cat alone, but see it as as only the ground floor of a higher and higher groupoid (paths, paths of paths, etc.) Rather than being the bedrock of Homotopy, model structures become models, or presentations, of the REAL OBJECT of Homotopy, the invariant infinity groupoid in all its splendor. That basic insight is already in Grothendieck, around 1983, maybe earlier, but has blossomed into an entire field thanks to Voevodsky, Lurie, ReskRezk, etc.

So, here is the key insight that migrates from the modern approach to the post-modern: do not look at a single cat alone, but see it as as only the ground floor of a higher and higher groupoid (paths, paths of paths, etc.) Rather than being the bedrock of Homotopy, model structures become models, or presentations, of the REAL OBJECT of Homotopy, the invariant infinity groupoid in all its splendor. That basic insight is already in Grothendieck, around 1983, maybe earlier, but has blossomed into an entire field thanks to Voevodsky, Lurie, Resk, etc.

So, here is the key insight that migrates from the modern approach to the post-modern: do not look at a single cat alone, but see it as as only the ground floor of a higher and higher groupoid (paths, paths of paths, etc.) Rather than being the bedrock of Homotopy, model structures become models, or presentations, of the REAL OBJECT of Homotopy, the invariant infinity groupoid in all its splendor. That basic insight is already in Grothendieck, around 1983, maybe earlier, but has blossomed into an entire field thanks to Voevodsky, Lurie, Rezk, etc.

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Mirco A. Mannucci
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Before Quillen, in 1958 1952 Steenrod and Eilenberg managed to get the Grand Unification of Cohomology, certainly a major breakthrough in the series of "foundational efforts" in Algebraic Topology.

Before Quillen, in 1958 Steenrod and Eilenberg managed to get the Grand Unification of Cohomology, certainly a major breakthrough in the series of "foundational efforts" in Algebraic Topology.

Before Quillen, in 1952 Steenrod and Eilenberg managed to get the Grand Unification of Cohomology, certainly a major breakthrough in the series of "foundational efforts" in Algebraic Topology.

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Mirco A. Mannucci
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More recently, another omissis is RHT Rational Homotopy Theory, by Daniel Quillen and Dennis Sullivan, which is not only an important tool for computing, but represents in a way both a significant contraction and a broadening of Homotopy Theory.

Anyway, let us keep this list. I would suggest one tiny emendation: extend your 50 years slightly, by five years, to include a true Annus Mirabilis (1967), namely the work of Quillen on Model Categories.

More recently, another omissis is RHT Rational Homotopy Theory, by Daniel Quillen and Dennis Sullivan, which is not only an important tool for computing, but represents in a way both a significant contraction and a broadening of Homotopy Theory.

Anyway, let us keep this list. I would suggest one tiny emendation: extend your 50 years slightly, by five years, to include a true Annus Mirabilis (1967), namely the work of Quillen on Model Categories.

I would suggest one tiny emendation: extend your 50 years slightly, by five years, to include a true Annus Mirabilis (1967), namely the work of Quillen on Model Categories.

David Quillen -> Daniel Quillen
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John Palmieri
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Mirco A. Mannucci
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Mirco A. Mannucci
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